]>
2016
9
6
ISSN 2008-1898
1503
Variational approach to second--order damped Hamiltonian systems with impulsive effects
Variational approach to second--order damped Hamiltonian systems with impulsive effects
en
en
In this paper, we consider the existence of second-order damped vibration Hamiltonian systems with
impulsive effects. We obtain some new existence theorems of solutions by using variational methods.
3459
3472
Jian
Liu
School of Mathematics and Quantitative Economics
Shandong University of Finance and Economics
China
kkword@126.com
Zengqin
Zhao
School of Mathematical Sciences
Qufu Normal University
China
zqzhaoy@163.com
Hamiltonian systems
variational method
impulsive effects
damped vibration.
Article.1.pdf
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[1]
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J. Liu, Z. Zhao, An application of variational methods to second-order impulsive differential equation with derivative dependence, Electron. J. Differential Equations, 2014 (2014), 1-13
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J. Mawhin, M. Willem, Critical Points Theory and Hamiltonian Systems, Springer-Verlag, New York (1989)
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J. J. Nieto , Variational formulation of a damped Dirichlet impulsive problem, Appl. Math. Lett., 23 (2010), 940-942
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J. J. Nieto, D. O'Regan, Variational approach to impulsive differential equations, Nonlinear Anal. Real World Appl., 10 (2009), 680-690
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P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Application to Differential Equations, American Mathematical Society, Providence, RI (1986)
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J. Sun, H. Chen, J. J. Nieto, M. Otero-Novoa, Multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects, Nonlinear Anal., 72 (2010), 4575-4586
##[8]
J. Sun, H. Chen, L. Yang , The existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method, Nonlinear Anal., 73 (2010), 440-449
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C. Tang, Periodic solutions of non-autonomous second order systems, J. Math. Anal. Appl., 202 (1996), 465-469
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X. Wu, Saddle point characterization and multiplicity of periodic solutions of non-autonomous second order systems, Nonlinear Anal., 58 (2004), 899-907
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J. Xiao, J. J. Nieto, Variational approach to some damped Dirichlet nonlinear impulsive differential equations, J. Franklin Inst., 348 (2011), 369-377
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J. Xiao, J. J. Nieto, Z. Luo , Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 426-432
##[16]
D. Zhang , Multiple solutions of nonlinear impulsive differential equations with Dirichlet boundary conditions via variational method, Results Math., 63 (2013), 611-628
##[17]
D. Zhang, B. Dai, Existence of solutions for nonlinear impulsive differential equations with Dirichlet boundary conditions, Math. Comput. Modelling, 53 (2011), 1154-1161
##[18]
J. Zhou, Y. Li , Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects, Nonlinear Anal., 72 (2010), 1594-1603
]
Some Oscillatory Properties for a Class of Partial Difference Equations
Some Oscillatory Properties for a Class of Partial Difference Equations
en
en
In this paper we study the oscillatory property of solutions for a class of partial difference equation with
constant coefficients. In order to study the oscillation results, we find the regions of nonexistence of positive
roots of its characteristic equation which is equivalent to the oscillation results. We derive some necessary
and sufficient conditions by means of the envelope theory.
3473
3478
Huili
Ma
Department of Mathematics
Northwest Normal University
P. R. China
mahuili@nwnu.edu.cn
Jiaofeng
Wang
Department of Mathematics
Northwest Normal University
P. R. China
wangjf0713@163.com
Partial difference equation
oscillation
envelope
characteristic equation.
Article.2.pdf
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R. P. Agarwal, S. R. Grace, D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht (2003)
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R. P. Agarwal, Y. Zhou , Oscillation of partial difference equations with continuous variables, Math. Comput. Modelling, 31 (2000), 17-29
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B. Zhang, Y. Zhou, Qualitative analysis of delay partial difference equations, Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York (2007)
]
Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays
Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays
en
en
In this paper, we consider a ratio-dependent predator-prey system with multiple delays where the dynamics
are logistic with the carrying capacity proportional to prey population. By choosing the sum \(\tau\)
of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of
Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the
bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem
for functional differential equations. Finally, some numerical simulations are carried out for illustrating the
theoretical results.
3479
3490
Dingyang
Lv
Department of Mathematics
Hunan First Normal College
P. R. China
dingyanglvmath@163.com
Wen
Zhang
School of Mathematics and Statistics
School of Mathematics and Statistics
Hunan University of Commerce
Central South University
P. R. China
P. R. China
zwmath2011@163.com
Yi
Tang
Department of Mathematics
Hunan First Normal College
P. R. China
929477429@qq.com
Ratio-dependent
delay
Hopf bifurcation
center manifold
periodic solutions.
Article.3.pdf
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[1]
C. Celik, The stability and Hopf bifurcation for a predator-prey system with time delay, Chaos Solitions Fractals, 37 (2008), 87-99
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C. Celik, Hopf bifurcation of a ratio-dependent predator-prey system with time delay, Chaos Solitions Fractals, 42 (2009), 1474-1484
##[3]
C. Celik, O. Duman, Allee effect in a discrete-time predator-prey system, Chaos Solitions Fractals, 40 (2009), 1956-1962
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D. Hadjiavgousti, S. Ichtiaroglou, Allee effect in a predator-prey system, Chaos Solitions Fractals, 36 (2008), 334-342
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G. Hu, W. Li, Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects, Nonlinear Anal. RWA, 11 (2010), 819-826
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Y. K. Li, T. W. Zhang, On the existence and stability of a unique almost periodic sequence solution in discrete predator-prey models with time delays, Appl. Math. Model., 35 (2011), 5448-5459
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Y. K. Li, K. H. Zhao, Y. Ye, Multiple positive periodic solutions of n species delay competition systems with harvesting terms, Nonlinear Anal. RWA, 12 (2011), 1013-1022
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Y. K. Li, L. F. Zhu, Positive periodic solutions for a class of higher-demensional state-dependent delay functional differential equations with feedback control , Appl. Math. Comput., 159 (2004), 783-795
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J. Liu, Y. K. Li, L. L. Zhao, On a periodic predator-prey system with time delays on time scales, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 3432-3438
##[19]
Y. Song, Y. Peng, J. Wei, Bifurcations for a predator-prey system with two delays, J. Math. Anal. Appl., 337 (2008), 466-479
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H. J. Sun, H. J. Cao, Bifurcations and chaos of a delayed ecological model, Chaos Solitions Fractals, 33 (2007), 1383-1393
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C. Xu, X. Tang, M. Liao, Stability and bifurcation analysis of a delayed predator-prey model of prey dispersal in two-patch environments, Appl. Math. Comput., 216 (2010), 2920-2936
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X. Yan, W. Li , Hopf bifurcation and global periodic solutions in a delayed predator-prey system, Appl. Math. Comput., 177 (2006), 427-445
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F. Q. Yin, Y. k. Li, Positive periodic solutions of a single species model with feedback regulation and distributed time delays, Appl. Math. Comput, 153 (2004), 475-484
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S. Zhou, Y. Liu, G. Wang , The stability of predator-prey systems subject to the Allee effects, Theor. Population Biol., 67 (2005), 23-31
]
Quantum difference Langevin equation with multi-quantum numbers q-derivative nonlocal conditions
Quantum difference Langevin equation with multi-quantum numbers q-derivative nonlocal conditions
en
en
In the present paper, we study a new class of boundary value problems for Langevin quantum difference
equations with multi-quantum numbers q-derivative nonlocal conditions. Some new existence and uniqueness
results are obtained by using standard fixed point theorems. The existence and uniqueness of solutions is
established by Banach's contraction mapping principle, while the existence of solutions is derived by using
Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Examples illustrating the
results are also presented.
3491
3503
Surang
Sitho
Department of Social and Applied Science, College of Industrial Technology
King Mongkut's University of Technology North Bangkok
Thailand
srg@kmutnb.ac.th
Sorasak
Laoprasittichok
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Thailand
sorasak_kmutnb@hotmail.com
Sotiris K.
Ntouyas
Department of Mathematics
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
University of Ioannina
King Abdulaziz University
Greece
Saudi Arabia
sntouyas@uoi.gr
Jessada
Tariboon
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Thailand
jessada.t@sci.kmutnb.ac.th
q-calculus
nonlocal conditions
Langevin equation
existence
fixed point.
Article.4.pdf
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[1]
B. Ahmad, Boundary value problems for nonlinear third-order q-difference equations, Electron. J. Diff. Equ., 2011 (2011), 1-7
##[2]
B. Ahmad, A. Alsaedi, S. K. Ntouyas, A study of second-order q-difference equations with boundary conditions, Adv. Difference Equ., 2012 (2012), 1-10
##[3]
B. Ahmad, P. Eloe, A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices, Comm. Appl. Nonlinear Anal., 17 (2010), 69-80
##[4]
B. Ahmad, J. J. Nieto, Basic theory of nonlinear third-order q-difference equations and inclusions, Math. Model. Anal., 18 (2013), 122-135
##[5]
B. Ahmad, J. J. Nieto, A. Alsaedi, M. El-Shahed, A study of nonlinear Langevin equation involving two fractional orders in different intervals, Nonlinear Anal. Real World Appl., 13 (2012), 599-606
##[6]
B. Ahmad, S. K. Ntouyas, Boundary value problems for q-difference inclusions , Abstr. Appl. Anal., 2011 (2011), 1-15
##[7]
M. H. Annaby, Z. S. Mansour, q-Fractional Calculus and Equations, Springer-Verlag, Berlin (2012)
##[8]
G. Bangerezako, Variational q-calculus, J. Math. Anal. Appl., 289 (2004), 650-665
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W. T. Coffey, Y. P. Kalmykov, J. T. Waldron, The Langevin equation. With applications to stochastic problems in physics, chemistry and electrical engineering: Second edition, World Scientific Publishing Co., Singapore (2004)
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M. El-Shahed, H. A. Hassan, Positive solutions of q-difference equation, Proc. Amer. Math. Soc., 138 (2010), 1733-1738
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R. A. C. Ferreira, Nontrivial solutions for fractional q-difference boundary value problems,, Electron. J. Qual. Theory Differ. Equ., 2010 (2010), 1-10
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G. Gasper, M. Rahman, Some systems of multivariable orthogonal q-Racah polynomials, Ramanujan J., 13 (2007), 389-405
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A. Granas, J. Dugundji, Fixed Point Theory, Springer-Verlag , New York (2003)
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V. Kac, P. Cheung, Quantum Calculus, Springer-Verlag, New York (2002)
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S. C. Lim, M. Li, L. P. Teo, Langevin equation with two fractional orders, Phys. Lett. A, 372 (2008), 6309-6320
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S. C. Lim, L. P. Teo, The fractional oscillator process with two indices, J. Physics A, 42 (2009), 1-34
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L. Lizana, T. Ambjörnsson, A. Taloni, E. Barkai, M. A. Lomholt, Foundation of fractional Langevin equation: Harmonization of a many-body problem, Phys. Rev. E, 81 (2010), 1-8
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A. Lozinski, R. G. Owens, T. N. Phillips, The Langevin and Fokker-Planck Equations in Polymer Rheology, Handb. Numer. Anal. , 16 (2011), 211-303
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J. Tariboon, S. K. Ntouyas, C. Thaiprayoon, Nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions, Adv. Math. Phys., 2014 (2014), 1-15
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M. Uranagase, T. Munakata, Generalized Langevin equation revisited: mechanical random force and self-consistent structure, J. Phys., 43 (2010), 1-11
]
New multivalued fixed point results in cone b--metric spaces
New multivalued fixed point results in cone b--metric spaces
en
en
In this paper, we give a fixed point theorem for multivalued mappings in a cone b-metric space without the
assumption of normality on cones and generalize some attractive results in recent literature.
3504
3510
Zhe
Chu
Department of Mathematics
Nanchang University
P. R. China
chuzhe@email.ncu.edu.cn
Xianjiu
Huang
Department of Mathematics
Nanchang University
P. R. China
xjhuangxwen@163.com
Xiaoyi
Liu
Department of Mathematics
Nanchang University
P. R. China
1210371418@qq.com
Fixed points
multivalued mappings
cone b-metric spaces.
Article.5.pdf
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations integrales, Fund. Math., 3 (1922), 133-181
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S. H. Cho, J. S. Bae , Fixed point theorems for multi-valued maps in cone metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-7
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L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
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N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces , Comput. Math. Appl., 62 (2011), 1677-1684
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M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69 (2008), 2942-2949
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G. Mot, A. Petrusel , Fixed point theory for a new type of contractive multivalued operators, Nonlinear Anal., 70 (2009), 3371-3377
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]
Some properties of the quasicompact-open topology on C(X)
Some properties of the quasicompact-open topology on C(X)
en
en
This paper introduces quasicompact-open topology on C(X) and compares this topology with the
compact-open topology and the topology of uniform convergence. Then it examines submetrizability, metrizability,
separability, and second countability of the quasicompact-open topology on C(X).
3511
3518
Deniz
Tokat
Department of Mathematics, Faculty of Arts and Sciences
Nevsehir Hacı Bektas Veli University
Turkey
dtokat@nevsehir.edu.tr
İsmail
Osmanoğlu
Department of Mathematics, Faculty of Arts and Sciences
Nevsehir Hacı Bektas Veli University
Turkey
ismailosmanoglu@yahoo.com
Function space
set-open topology
compact-open topology
quasicompactness
separability
submetrizability
second countability.
Article.6.pdf
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A. T. Al-Ani, Countably z-compact spaces, Arch. Math. (Brno), 50 (2014), 97-100
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S. Kundu, P. Garg, The pseudocompact-open topology on C(X), Topology Proc., 30 (2006), 279-299
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]
Generalized k-Mittag-Leffler function and its composition with pathway integral operators
Generalized k-Mittag-Leffler function and its composition with pathway integral operators
en
en
Our purpose in this paper is to consider a more generalized form of the Mittag-Leffler function. For this
newly defined function, we obtain certain composition formulas with pathway fractional integral operators.
We also point out some important special cases of the main results.
3519
3526
K. S.
Nisar
Department of Mathematics, College of Arts and Science
Prince Sattam bin Abdulaziz University
Saudi Arabia
ksnisar1@gmail.com
S. D.
Purohit
Department of HEAS (Mathematics)
Rajasthan Technical University
India
sunil_a_purohit@yahoo.com
M. S.
Abouzaid
Department of Mathematics, Faculty of Science
Kafrelshiekh University
Egypt
moheb_abouzaid@hotmail.com
M.
Al Qurashi
Department of Mathematics
King Saud University
Saudi Arabia
maysaa@ksu.edu.sa
D.
Baleanu
Department of Mathematics
Institute of Space Sciences
Cankaya University
Magurele-Bucharest
Turkey
Romania
dumitru@cankaya.edu.tr
Mittag-Leffler functions
pathway integral operator.
Article.7.pdf
[
[1]
P. Agarwal, S. D. Purohit, The unified pathway fractional integral formulae , J. Fract. Calc. Appl., 4 (2013), 1-8
##[2]
D. Baleanu, P. Agarwal, A composition formula of the pathway integral transform operator, Note Mat., 34 (2014), 145-155
##[3]
D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods , World Sci., 3 (2012), 10-16
##[4]
G. A. Dorrego, R. A. Cerutti , The k-Mittag-Leffer function, Int. J. Contemp. Math. Sci., 7 (2012), 705-716
##[5]
K. S. Gehlot , The Generalized k-Mittag-Leffer function, Int. J. Contemp. Math. Sci., 7 (2012), 2213-2219
##[6]
M. A. Khan, S. Ahmed , On some properties of the generalized Mittag-Leffer function, Springer Plus, 2 (2013), 1-9
##[7]
A. M. Mathai, A pathway to matrix-variate gamma and normal densities, Linear Algebra Appl., 396 (2005), 317-328
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A. M. Mathai, H. J. Haubold, Pathway model, superstatistics, Tsallis statistics and a generalize measure of entropy, Phys. A, 375 (2007), 110-122
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A. M. Mathai, H. J. Haubold , On generalized distributions and path-ways, Phys. Lett. A, 372 (2008), 2109-2113
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G. M. Mittag-Leffer , Sur la nouvelle fonction \(E_\alpha(x)\) , CR Acad. Sci. Paris, 137 (1903), 554-558
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G. M. Mittag-Leffer , Sur la representation analytique d'une branche uniforme d'une function monogene, Acta Math., 29 (1905), 101-181
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S. S. Nair, Pathway fractional integration operator, Fract. Calc. Appl. Anal., 12 (2009), 237-252
##[13]
K. S. Nisar, S. R. Mondal, P. Agarwal, Pathway fractional integral operator associated with Struve function of first kind, Adv. Stud. Contemp. Math., 26 (2016), 63-70
##[14]
K. S. Nisar, S. D. Purohit, S. R. Mondal, Generalized fractional kinetic equations involving generalized Struve function of the first kind, J. King Saud Univ. Sci., 28 (2016), 167-171
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T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffer function in the Kernel, Yokohama Math. J., 19 (1971), 7-15
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I. Podlubny, Fractional Differential Equations. An introduction to fractional derivatives, fractional di erential equations, to methods of their solution and some of their applications, Academic Press, San Diego, CA (1999)
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C. Ram, P. Choudhary, Pathway fractional integration operator as generalized k-mittag-leffer function in its kernel, Int. J. Math. Arch., 4 (2014), 114-120
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]
Some common coupled fixed point results in two S-metric spaces and applications to integral equations
Some common coupled fixed point results in two S-metric spaces and applications to integral equations
en
en
The purpose of this paper is to prove some new coupled common fixed point theorems for mappings
defined on a set equipped with two S-metrics. We also provide illustrative examples in support of our new
results. Meantime, we give an existence and uniqueness theorem of solution for a class of nonlinear integral
equations by using the obtained result.
3527
3544
Liya
Liu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
846883245@qq.com
Feng
Gu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
gufeng_99@sohu.com
S-metric space
contractive mappings
coupled coincidence point
coupled common fixed point
mixed g-monotone property.
Article.8.pdf
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[1]
J. M. Afra, Fixed point type theorem in S-metric spaces, Middle-East J. Sci. Res., 22 (2014), 864-869
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J. M. Afra , Fixed point type theorem for weak contraction in S-metric spaces, Int. J. Res. Rev. Appl. Sci., 22 (2015), 11-14
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J. M. Afra, Double contraction in S-metric spaces , Int. J. Math. Anal., 9 (2015), 117-125
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T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
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P. Chouhan, N. Malviya, A common unique fixed point theorem for expansive type mappings in S-metric spaces, Int. Math. Forum, 8 (2013), 1287-1293
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F. Gu, Z. Yang, Some new common fixed point results for three pairs of mappings in generalized metric spaces, Fixed point Theory Appl., 2013 (2013), 1-21
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V. Gupta, R. Deep, Some coupled fixed point theorems in partially ordered S-metric spaces, Miskolc Math. Notes, 16 (2015), 181-194
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H. Raj, N. Hooda, Coupled fixed point theorems S-metric spaces with mixed g-monotone property, Int. J. Emerging Trends Eng. Dev., 4 (2014), 68-81
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]
Analytic solution of generalized space time advection-dispersion equation with fractional Laplace operator
Analytic solution of generalized space time advection-dispersion equation with fractional Laplace operator
en
en
The aim of this paper is to investigate the solutions of Time-space fractional advection-dispersion equation
with Hilfer composite fractional derivative and the space fractional Laplacian operator. The solution of
the equation is obtained by applying the Laplace and Fourier transforms, in terms of Mittag-leffler function.
The work by R. K. Saxena (2010) and Haung and Liu (2005) follows as particular case of our results.
3545
3554
Ritu
Agarwal
Department of Mathematics
Malaviya National Institute of Technology
India
ragarwal.maths@mnit.ac.in
Sonal
Jain
Department of Mathematics
Malaviya National Institute of Technology
India
sonaljainmnit@gmail.com
R. P.
Agarwal
Department of Mathematics
Texas A & M University
agarwal@tamuk.edu
Time-space fractional advection-dispersion equation
Fourier transform
Laplace transform
composite fractional derivative
H-function
Mittag-Leffler function
fractional Laplace operator.
Article.9.pdf
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D. A. Benson, S. W. Wheatcraft, M. M. Meerschaert, Application of a fractional advection-dispersion equation, Water Resources Research, 36 (2000), 1403-1412
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R. K. Saxena, R. Saxena, S. L. Kalla , Solution of the space-time fractional Schrödinger equation equation occuring in quantum mechanics, Fract. Calc. Appl. Anal., 13 (2010), 177-190
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]
The stability of sextic functional equation in fuzzy modular spaces
The stability of sextic functional equation in fuzzy modular spaces
en
en
By using the fixed point technique, we prove the stability of sixtic functional equations. Our results
are studied and proved in the framework of fuzzy modular spaces (brie
y, FM-spaces). The lower semi
continuous (brie
y, l.s.c.) and \(\beta\)-homogeneous are necessary conditions for this work.
3555
3569
Kittipong
Wongkum
Department of Mathematics, Faculty of Science
Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
King Mongkut's University of Technology Thonburi (KMUTT)
King Mongkut's University of Technology Thonburi (KMUTT)
Thailand
Thailand
kittipong.wong@mail.kmutt.ac.th
Poom
Kumam
Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
Department of Mathematics, Faculty of Science
Department of Medical Research
King Mongkut's University of Technology Thonburi (KMUTT)
King Mongkut's University of Technology Thonburi (KMUTT)
China Medical University Hospital, China Medical University
Thailand
Thailand
Taiwan
poom.kum@kmutt.ac.th
Stability
sextic mapping
fuzzy modular space.
Article.10.pdf
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X. Arul Selvaraj, D. Sivakumar , t-Norm (\(\lambda,\mu\))-Fuzzy Quotient Near-Rings and t-Norm (\(\lambda,\mu\))-Fuzzy Quasi-Ideals, Int. Math. Forum, 6 (2011), 203-209
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Y. J. Cho, M. B. Ghaemi, M. Choubin, M. E. Gordji , On the Hyers-Ulam stability of sextic functional equations in \(\beta\)-homogeneous probabilistic modular spaces, Math. Inequal. Appl., 4 (2013), 1097-1114
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]
Important inequalities for preinvex functions
Important inequalities for preinvex functions
en
en
The paper deals with fundamental inequalities for preinvex functions. The result relating to preinvex
functions on the invex set that satisfies condition C shows that such functions are convex on every generated
line segment. As an effect of that convexity, the paper provides symmetric forms of the most important
inequalities which can be applied to preinvex functions.
3570
3579
Zlatko
Pavic
Mechanical Engineering Faculty in Slavonski Brod
University of Osijek
Croatia
Zlatko.Pavic@sfsb.hr
Shanhe
Wu
Department of Mathematics
Longyan University
P. R. China
shanhewu@163.com
Vedran
Novoselac
Mechanical Engineering Faculty in Slavonski Brod
University of Osijek
Croatia
Vedran.Novoselac@sfsb.hr
Preinvex function
convex function
inequality.
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Ch. Hermite, Sur deux limites d'une intégrale définie, Mathesis, 3 (1883), 1-82
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I. Iscan , Hermite-Hadamard's inequalities for preinvex functions via fractional integrals and related fractional inequalities, American J. Math. Anal., 1 (2013), 33-38
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I. Iscan, S. Wu , Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014), 237-244
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S. Wu, B. Sroysang, J.-S. Xie, Y. M. Chu , Parametrized inequality of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex, SpringerPlus, 2015 (2015), 1-9
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]
Stabilization control of generalized type neural networks with piecewise constant argument
Stabilization control of generalized type neural networks with piecewise constant argument
en
en
The generalized type neural networks have always been a hotspot of research in recent years. This paper
concerns the stabilization control of generalized type neural networks with piecewise constant argument.
Through three types of stabilization control rules (single state stabilization control rule, multiple state
stabilization control rule and output stabilization control rule), together with the estimate of the state
vector with piecewise constant argument, several succinct criteria of stabilization are derived. The obtained
results improve and extend some existing results. Two numerical examples are proposed to substantiate the
effectiveness of the theoretical results.
3580
3599
Liguang
Wan
College of Mechatronics and Control Engineering
Hubei Normal University
China
Ailong
Wu
hbnuwu@yeah.net
Hubei Normal University
China
hbnuwu@yeah.net
Generalized type systems
neural networks
state stabilization
output stabilization.
Article.12.pdf
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[1]
M. U. Akhmet, On the reduction principle for differential equations with piecewise constant argument of generalized type, J. Math. Anal. Appl., 336 (2007), 646-663
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M. U. Akhmet, Almost periodic solutions of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. Hybrid Syst., 2 (2008), 456-467
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M. U. Akhmet, Stability of differential equations with piecewise constant arguments of generalized type, Nonlinear Anal., 68 (2008), 794-803
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M. U. Akhmet, D. Arugaslan, Lyapunov-Razumikhin method for differential equations with piecewise constant argument, Discrete Contin. Dyn. Syst, 25 (2009), 457-466
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M. U. Akhmet, D. Arugaslan, E. Yılmaz, Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Netw., 23 (2010), 805-811
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M. U. Akhmet, D. Arugaslan, E. Yımlaz, Stability in cellular neural networks with piecewise constant argument, J. Comput. Appl. Math., 233 (2010), 2365-2373
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M. U. Akhmet, E. Yımlaz, Impulsive Hopfield-type neural network system with piecewise constant argument, Nonlinear Anal. Real World Appl., 11 (2010), 2584-2593
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P. Balasubramaniam, G. Nagamani , Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays, Nonlinear Anal. Hybrid Syst., 4 (2010), 853-864
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G. Bao, S. P. Wen, Z. G. Zeng, Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type, Neural Netw., 33 (2012), 32-41
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W. H. Chen, X. M. Lu, Z. H. Guan, W. X. Zheng, Delay-dependent exponential stability of neural networks with variable delay: an LMI approach, IEEE Trans. Circuit Syst. II Expr. Bri., 53 (2006), 837-842
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W. H. Chen, X. M. Lu, W. X. Zhen, Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks, IEEE Trans. Neural Netw. Learn Syst., 26 (2015), 734-748
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W. H. Chen, S. X. Luo, Multistability in a class of stochastic delayed Hopfield neural networks, Neural Netw., 68 (2015), 52-61
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F. Fourati, M. Chtourou, M. Kamoun, Stabilization of unknown nonlinear systems using neural networks, Appl. Soft Comput., 8 (2008), 1121-1130
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Z. Y. Guo, J. Wang, Global exponential synchronization of two memristor-baesd recurrent neural networks with time delays via static or dynamic coupling, IEEE Trans. Syst., Man, Cybern. B., Cybern, 45 (2015), 235-249
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C. Hua, X. Guan, Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks, IEEE Trans. Neural Netw., 19 (2008), 673-688
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T. W. Huang, Exponential stability of fuzzy cellular neural networks with distributed delay, Phys. Lett. A., 351 (2006), 48-52
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C. X. Huang, J. Cao, Convergence dynamics of stochastic Cohen-Crossberg neural networks with unbounded distributed delays, IEEE Trans. Neural Netw., 22 (2011), 561-572
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E. Kaslik, S. Sivasundaram, Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis, Neural Netw., 24 (2011), 370-377
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T. Li, A. G. Song, S. M. Fei, T. Wang, Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay, IEEE Trans. Neural Netw., 21 (2010), 1365-1371
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C. D. Li, S. C.Wu, G. G. Feng, X. F. Liao, Stabilizing effects of impulses in discrete-time delayed neural networks, IEEE Trans. Neural Netw., 22 (2011), 323-329
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X. F. Liao, G. Chen, E. N. Sanchez, Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach, Neural Netw., 15 (2002), 855-866
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Z. Q. Liu, R. E. Torres, N. Patel, Q. J. Wang, Further development of input-to-state stabilizing control for dynamic neural network systems, IEEE Trans. Syst. Man Cybern. A., 38 (2008), 1425-1433
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F. Long, S. M. Fei , Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems, Neurocomputing, 71 (2008), 1741-1747
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K. Patan, Stability analysis and the stabilization of a class of discretetime dynamic neural networks, IEEE Trans. Neural Netw, 18 (2007), 660-673
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V. N. Phat, H. Trinh , Exponential stabilization of neural networks with various activation functions and mixed time-varying delays, IEEE Trans. Neural Netw., 21 (2010), 1180-1184
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Y. Shen, J. Wang , Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters, IEEE Trans. Neural Netw, 18 (2007), 1857-1862
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Y. Shen, J. Wang, Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances, IEEE Trans. Neural Netw. Learn Syst., 23 (2012), 87-96
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Q. K. Song, J. Cao, Passivity of uncertain neural networks with both leakage delay and time-varying delay, Nonlinear Dyn., 67 (2012), 1695-1707
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A. L. Wu, Z. G. Zeng, Exponential stabilization of memristive neural networks with time delays, IEEE Trans. Neural Netw. Learn Syst., 23 (2012), 1919-1929
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A. L. Wu, Z. G. Zeng , Lagrange stability of memristive neural networks with discrete and distributed delays, IEEE Trans. Neural Netw. Learn Syst., 25 (2014), 690-703
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A. L. Wu, Z. G. Zeng, New global exponential stability results for memristive neural system with time-varying delays, Neurocomputing, 144 (2014), 553-559
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J. Xiao, Z. G. Zeng, S. P. Wen, A. L. Wu, Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions, Nonlinear Dyn., 74 (2013), 213-225
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Z. G. Zeng, D. S. Huang, Pattern memory analysis based on stability theory of cellular neural networks, Appl. Math. Model., 32 (2008), 112-121
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Z. G. Zeng, J. Wang, Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , Neural Netw., 19 (2006), 1528-1537
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Z. G. Zeng, W. X. Zheng, Multistability of two kinds of recurrent neural networks with activation funtions symmetrical about the origin on the phase plane, IEEE Trans Neural Netw Learn Syst., 24 (2013), 1749-1762
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Z. Y. Zhang, C. Lin, B. Chen, Global stability criterion for delayed complex-valued recurrent neural networks, IEEE Trans. Neural Netw. Learn Syst., 25 (2014), 1704-1708
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X. L. Zhu, Y. Y. Wang , Stabilization for sampled-data neural-network-based control systems, IEEE Trans. Syst., Man, Cybern B., Cybern, 41 (2011), 210-221
]
The sequence asymptotic average shadowing property and transitivity
The sequence asymptotic average shadowing property and transitivity
en
en
Let \(X\) be a compact metric space and \(f\) be a continuous map from \(X\) into itself. In this paper, we
introduce the concept of the sequence asymptotic average shadowing property, which is a generalization
of the asymptotic average shadowing property. In the sequel, we prove some properties of the sequence
asymptotic average shadowing property and investigate the relationship between the sequence asymptotic
average shadowing property and transitivity.
3600
3610
Tao
Wang
Department of Mathematics
Nanchang University
P. R. China
taowangmath@163.com
Jiandong
Yin
Department of Mathematics
Nanchang University
P. R. China
yjdaxf@163.com
Qi
Yan
Department of Mathematics
Nanchang University
P. R. China
qiyanmath@163.com
Sequence asymptotic average shadowing property
chain transitive
weakly almost periodic point
transitivity
weakly mixing.
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M. L. Blank, Metric properties of \(\epsilon\)-trajectories of dynamical systems with stochastic behavior, Ergodic Theory Dynam. Systems, 8 (1988), 365-378
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M. L. Blank, Deterministic properties of stochastically perturbed dynamical systems, Theory Probab. Appl., 33 (1988), 612-623
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R. B. Gu, The asymptotic average shadowing property and transitivity, Nonlinear Anal., 67 (2007), 1680-1689
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R. B. Gu, On ergodicity of systems with the asymptotic average shadowing property, Comput. Math. Appl., 55 (2008), 1137-1141
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Y. X. Niu, S. B. Su, On strong ergodicity and chaoticity of systems with the asymptotic average shadowing property, Chaos Solitons Fractals, 44 (2011), 429-432
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An extension of Caputo fractional derivative operator and its applications
An extension of Caputo fractional derivative operator and its applications
en
en
In this paper, an extension of Caputo fractional derivative operator is introduced, and the extended
fractional derivatives of some elementary functions are calculated. At the same time, extensions of some
hypergeometric functions and their integral representations are presented by using the extended fractional
derivative operator, linear and bilinear generating relations for extended hypergeometric functions are obtained,
and Mellin transforms of some extended fractional derivatives are also determined.
3611
3621
İ. Onur
Kıymaz
Dept. of Mathematics
Ahi Evran Univ.
Turkey
iokiymaz@ahievran.edu.tr
Ayşegül
Çetinkaya
Dept. of Mathematics
Ahi Evran Univ.
Turkey
acetinkaya@ahievran.edu.tr
Praveen
Agarwal
Dept. of Mathematics
Anand International College of Eng.
India
goyal.praveen2011@gmail.com
Caputo fractional derivative
hypergeometric functions
generating functions
Mellin transform
integral representations.
Article.14.pdf
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M. Ali Özarslan, E. Özergin, Some generating relations for extended hypergeometric functions via generalized fractional derivative operator, Math. Comput. Modelling, 52 (2010), 1825-1833
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X. J. Yang, D. Baleanu, H. M. Srivastava, Local fractional integral transforms and their applications, Academic Press, Amsterdam (2016)
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X. J. Yang, H. M. Srivastava, An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives, Commun. Nonlinear Sci. Numer. Simul., 29 (2015), 499-504
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X. J. Yang, H. M. Srivastava, J. A. Machado, A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow, arXiv preprint, (2016)
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X. J. Yang, J. A. Tenreiro Machado , A new insight into complexity from the local fractional calculus view point: modelling growths of populations, Math. Meth. Appl. Sci., 2015 (2015), 1-6
]
Boundary value problems for fractional differential equations with integral and ordinary-fractional flux boundary conditions
Boundary value problems for fractional differential equations with integral and ordinary-fractional flux boundary conditions
en
en
In this paper, we consider a new class of boundary value problems of Caputo type fractional differential
equations supplemented with classical/nonlocal Riemann-Liouville integral and
flux boundary conditions
and obtain some existence results for the given problems. The
flux boundary condition \(x'(0) = b ^cD^\beta x(1)\)
states that the ordinary
flux \(x'(0)\) at the left-end point of the interval [0; 1] is proportional to a
flux \(^cD^\beta x(1)\)
of fractional order \(\beta \in (0; 1]\) at the right-end point of the given interval. The coupling of integral and
flux
boundary conditions introduced in this paper owes to the novelty of the work. We illustrate our results with
the aid of examples. Our work not only generalizes some known results but also produces new results for
specific values of the parameters involved in the problems at hand.
3622
3637
Bashir
Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
bashirahmadqau@yahoo.com
Sotiris K.
Ntouyas
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
Department of Mathematics
King Abdulaziz University
University of Ioannina
Saudi Arabia
Greece
sntouyas@uoi.gr
Differential equations
ractional order
integral boundary conditions
flux
existence
fixed point.
Article.15.pdf
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R. P. Agarwal, M. Benchohra, S. Hamani , A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions , Acta Appl. Math., 109 (2010), 973-1033
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]
Some new properties of generalized Hölders inequalities
Some new properties of generalized Hölders inequalities
en
en
Hölder's inequality and its various generalizations are playing very important and basic role in different
branches of modern mathematics. In this paper, we give some new monotonicity properties of generalized
Hölder's inequalities and then we obtain some new refinements of generalized Hölder's inequalities.
3638
3646
Jing-Feng
Tian
College of Science and Technology
North China Electric Power University
P. R. China
tianjfhxm_ncepu@163.com
Ming-Hu
Ha
School of Science
Hebei University of Engineering
P. R. China
mhhhbu@163.com
Generalized Hölder's inequality
Hölder's inequality
monotonicity properties
refinements.
Article.16.pdf
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]
Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer
Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer
en
en
The power law has been used to construct the derivative with fractional order in Caputo and Riemann-
Liouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law
behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based
upon the generalized Mittag-Leffler function, since the Mittag-Leffler function is more suitable in expressing
nature than power function. In this paper, we applied their new finding to the model of groundwater
flowing
within an unconfined aquifer.
3647
3654
Rubayyi T.
Alqahtani
Department of Mathematics and Statistics, College of Science
Al-Imam Mohammad Ibn Saud Islamic University (IMSIU)
Saudi Arabia
rtalqahtani@imamu.edu.sa
Atangana-Baleanu derivatives
Laplace transforms
groundwater flow
unconfined aquifer.
Article.17.pdf
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[1]
A. Atangana, On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation, Appl. Math. Comput., 273 (2016), 948-956
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A. Atangana, B. S. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, Entropy, 17 (2015), 4439-4453
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A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Therm. Sci., 20 (2016), 763-769
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A. Atangana, D. Baleanu, Caputo-Fabrizio Derivative Applied to Groundwater Flow within Confined Aquifer, J. Eng. Mech, 2016, 5 pages. (2016)
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A. Atangana, N. Bildik, The Use of Fractional Order Derivative to Predict the Groundwater Flow, Math. Prob. Eng., 2013 (2013), 1-9
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A. Atangana, I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, (in press), -
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]
Common fixed point theorems for four mappings on cone b-metric spaces over Banach algebras
Common fixed point theorems for four mappings on cone b-metric spaces over Banach algebras
en
en
The purpose of this paper is to obtain several common fixed point theorems for four mappings in the
setting of cone b-metric spaces over Banach algebras. The obtained results generalize, complement, and
improve some results in the literature. Moreover, we give some supportive examples for our conclusions. In
addition, an application in the solution of a class of equations is given to illustrate the superiority of the
main results.
3655
3671
Huaping
Huang
School of Mathematics and Statistics
Hubei Normal University
China
mathhhp@163.com
Songlin
Hu
School of Mathematics and Statistics
Hubei Normal University
China
415027545@qq.com
Branislav Z.
Popović
Faculty of Science
University of Kragujevac
Serbia
bpopovic@kg.ac.rs
Stojan
Radenović
Faculty of Mechanical Engineering
Department of Mathematics
University of Belgrade
University of Novi Pazar
Serbia
Serbia
radens@beotel.net
Cone b-metric space over Banach algebra
c-sequence
weakly compatible
common fixed point.
Article.18.pdf
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[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420
##[2]
M. Abbas, B. E. Rhoades, T. Nazir, Common fixed points for four maps in cone metric spaces, Appl. Math. Comput., 216 (2010), 80-86
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A. Azam, I. Beg, M. Arshad, Fixed points in topological vector space-valued cone metric spaces, Fixed Point Theory Appl., 2010 (2010), 1-9
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I. Beg, A. Azam, M. Arshad, Common fixed points for maps in topological vector spaces valued cone metric spaces, Int. J. Math. Sci., 2009 (2009), 1-8
##[5]
M. Cvetkovic, V. Rakocevic, Quasi-contraction of Perov type, Appl. Math. Comput., 237 (2014), 712-722
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A. S. Cvetkovic, M. P. Stanic, S. Dimitrijevic, S. Simic, Common fixed point theorems for four mappings on cone metric type space, Fixed Point Theory Appl., 2011 (2011), 1-15
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W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259-2261
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W.-S. Du, E. Karapinıar, A note on cone b-metric and its related results: generalizations or equivalence, Fixed Point Theory Appl., 2013 (2013), 1-7
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Z. Ercan, On the end of the cone metric spaces, Topology Appl., 166 (2014), 10-14
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Y. Feng, W. Mao, The equivalence of cone metric spaces and metric spaces, Fixed Point Theory, 11 (2010), 259-264
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H. Huang, S. Radenovic , Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications, J. Nonlinear Sci. Appl., 8 (2015), 787-799
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H. Huang, S. Radenovic, Some fixed point results of generalized Lipschitz mappings on cone b-metric spaces over Banach algebras, J. Comput. Anal. Appl., 20 (2016), 566-583
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H. Huang, S. Radenovic, D. Ðoric , A note on the equivalence of some metric and H-cone metric fixed point theorems for multivalued contractions, Fixed Point Theory Appl., 2015 (2015), 1-8
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H. Huang, S. Xu, H. Liu, S. Radenovic, Fixed point theorems and T-stability of Picard iteration for generalized Lipschitz mappings in cone metric spaces over Banach algebras, J. Comput. Anal. Appl., 20 (2016), 869-888
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L.-G Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
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N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684
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]
An improved simulated annealing algorithm for bilevel multiobjective programming problems with application
An improved simulated annealing algorithm for bilevel multiobjective programming problems with application
en
en
In this paper, an improved simulated annealing (SA) optimization algorithm is proposed for solving
bilevel multiobjective programming problem (BLMPP). The improved SA algorithm uses a group of points
in its operation instead of the classical point-by-point approach, and the rule for accepting a candidate
solution that depends on a dominance based energy function is adopted in this algorithm. For BLMPP, the
proposed method directly simulates the decision process of bilevel programming, which is different from most
traditional algorithms designed for specific versions or based on specific assumptions. Finally, we present six
different test problems to measure and evaluate the proposed algorithm, including low dimension and high
dimension BLMPPs. The experimental results show that the proposed algorithm is a feasible and efficient
method for solving BLMPPs.
3672
3685
Tao
Zhang
School of Information and Mathematics
Yangtze University
China
Zhong
Chen
School of Information and Mathematics
Yangtze University
China
Yue
Zheng
School of Management
Huaibei Normal University
China
Jiawei
Chen
School of Mathematics and Statistics
College of Computer Science
Southwest University
Chongqing University
China
China
J.W.Chen713@163.com
Bilevel multiobjective programming
simulated annealing algorithm
Pareto optimal solution
elite strategy.
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J. Chen, Q. H. Ansari, Y. C. Liou, J. C. Yao, A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems, Comput. Opti. Appl., 2016 (2016), 1-20
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J. Chen, Y. C. Liou, C. F. Wen, Bilevel vector pesudomonotone equilibrium problem: duality and existence, J. Nonlinear Convex Anal., 16 (2015), 1293-1303
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B. Colson, P. Marcotte, G. Savard , Bilevel programming: A survey, A Quarterly J. Oper. Res., 3 (2005), 87-107
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K. Deb, Multi-Objective Optimization using evolutionary algorithms, IEEE Trans. Evolutionary Comput., 6 (2002), 182-197
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K. Deb, A. Sinha, Constructing test problems for bilevel evolutionary multi-objective optimization, IEEE Congr. Evolutionary Comput., (2009), 1153-1160
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R. L. Yang, J. F. Gu, An eficient simulated annealing algorithm for global optimization, Syst. Eng.-Theory Practice (in Chinese), 17 (1997), 30-36
##[41]
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##[42]
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G. Zhang, J. Lu, Fuzzy bilevel programming with multiple objectives and cooperative multiple followers, J. Global Optim., 47 (2010), 403-419
]
Fixed points in modular spaces via \(\alpha\)-admissible mappings and simulation functions
Fixed points in modular spaces via \(\alpha\)-admissible mappings and simulation functions
en
en
In this paper, by using the concepts of \(\alpha\)-admissible mappings and simulation functions, we establish
some fixed point results in the class of modular spaces. Our presented results generalize and improve many
known results in literature. Some concrete examples are also provided to support the obtained results.
3686
3701
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Abdelbasset
Felhi
Department of Mathematics and Statistics, College of Sciences
King Faisal University
Saudi Arabia
afelhi@kfu.edu.sa
Modular space
fixed point
simulation functions
\(\alpha\)-admissible mappings.
Article.20.pdf
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[1]
H. Argoubi, B. Samet, C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (2015), 1082-1094
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B. Samet, C. Vetro, P. Vetro , Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[21]
P. Turpin, Fubini inequalities and bounded multiplier property in generalized modular spaces, Special issue dedicated to Wladyslaw Orlicz on the occasion of his seventy-fifth birthday, Comment. Math., Special issue , 1 (1978), 331-353
]
Algorithms for finding minimum norm solution of equilibrium and fixed point problems for nonexpansive semigroups in Hilbert spaces
Algorithms for finding minimum norm solution of equilibrium and fixed point problems for nonexpansive semigroups in Hilbert spaces
en
en
In this paper, we introduce two general algorithms (one implicit and one explicit) for finding a common
element of the set of an equilibrium problem and the set of common fixed points of a nonexpansive semigroup
\(\{T(s)\}_{s\geq 0}\) in Hilbert spaces. We prove that both approaches converge strongly to a common element \(x^*\) of
the set of the equilibrium points and the set of common fixed points of \(\{T(s)\}_{s\geq 0}\). Such common element \(x^*\)
is the unique solution of some variational inequality, which is the optimality condition for some minimization
problem. As special cases of the above two algorithms, we obtain two schemes which both converge strongly
to the minimum norm element of the set of the equilibrium points and the set of common fixed points
of \(\{T(s)\}_{s\geq 0}\). The results obtained in the present paper improve and extend the corresponding results by
Cianciaruso et al. [F. Cianciaruso, G. Marino, L. Muglia, J. Optim. Theory. Appl., 146 (2010), 491-509]
and many others.
3702
3718
Yaqiang
Liu
School of Management, Tianjin Polytechnic University, Tianjin 300387, China.
Shin Min
Kang
Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea.
Youli
Yu
School of Mathematics and Information Engineering, Taizhou University, Linhai 317000, China.
Lijun
Zhu
School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China.
Equilibrium problem
variational inequality
fixed point
nonexpansive semigroup
algorithm
minimum norm.
Article.21.pdf
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V. Colao, G. L. Acedo, G. Marino, An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings, Nonlinear Anal., 71 (2009), 2708-2715
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J. C. Yao, Variational inequalities with generalized monotone operators, Math. Oper. Res., 19 (1994), 691-705
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Y. Yao, Y. J. Cho, Y.-C. Liou, Iterative algorithms for hierarchical fixed points problems and variational inequalities, Math. Comput. Modelling, 52 (2010), 1697-1705
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Y. Yao, Y. J. Cho, Y. C. Liou, Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems approach to optimization problems, Cent. Eur. J. Math., 9 (2011), 640-656
##[25]
Y. Yao, M. A. Noor, Y.-C. Liou, S. M. Kang, Iterative algorithms for general multivalued variational inequalities, Abstr. Appl. Anal., 2012 (2012), 1-10
##[26]
Y. Yao, M. A. Noor, K. I. Noor, Y.-C. Liou, H. Yaqoob, Modified extragradient method for a system of variational inequalities in Banach spaces, Acta Appl. Math., 110 (2010), 1211-1224
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L.-C. Zeng, J.-C. Yao, Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems, Taiwanese J. Math., 10 (2006), 1293-1303
]
A modified iterative algorithm for nonexpansive mappings
A modified iterative algorithm for nonexpansive mappings
en
en
A modified iterative algorithm is presented based on the semi-implicit midpoint rule. Strong convergence
analysis is demonstrated. Our method gives a unified framework related to the implicit midpoint rule. Our
results improve and extend the corresponding results in the literature.
3719
3726
Youli
Yu
School of Mathematics and Information Engineering
Taizhou University
China
yani3115791@126.com
Ching-Feng
Wen
Center for Fundamental Science and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
smkang@gnu.ac.kr
Nonexpansive mapping
implicit midpoint rule
fixed point.
Article.22.pdf
[
[1]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H. K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), 1-9
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H. H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl., 202 (1996), 150-159
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L. C. Ceng, A. Petrusel, J. C. Yao, Strong Convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudocontractive mappings , Appl. Math. Comput., 209 (2009), 162-176
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S. S. Chang, Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 323 (2006), 1402-1416
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C. E. Chidume, C. O. Chidume, Iterative approximation of fixed points of nonexpansive mappings, J. Math. Anal. Appl., 318 (2006), 288-295
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Y. J. Cho, X. Qin , Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces, J. Comput. Appl. Math., 228 (2009), 458-465
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F. Cianciaruso, G. Marino, L. Muglia, Y. Yao, on a two-steps algorithm for hierarchical fixed points problems and variational inequalities, J. Inequal. Appl., 2009 (2009), 1-13
##[9]
F. Cianciaruso, G. Marino, L. Muglia, Y. Yao, A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem, Fixed Point Theory Appl., 2010 (2010), 1-19
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K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, Cambridge (1990)
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T. H. Kim, H. K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal., 61 (2005), 51-60
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W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510
##[15]
C. H. Morales, J. S. Jung, Convergence of paths for pseudo-contractive mappings in Banach spaces, Proc. Amer. Math. Soc., 128 (2000), 3411-3419
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A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
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A. Petrusel, J. C. Yao, Viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings, Nonlinear Anal., 69 (2008), 1100-1111
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K. Shimoji, W. Takahashi, Strong convergence to common fixed points of infinite nonexpansive mappings and applications, Taiwanese J. Math., 5 (2001), 387-404
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T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl., 2005 (2005), 103-123
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H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
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H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[22]
H. K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-12
##[23]
Y. Yao, A general iterative method for a finite family of nonexpansive mappings, Nonlinear Anal., 66 (2007), 2676-2687
##[24]
Y. Yao, R. Chen, J. C. Yao, Strong convergence and certain control conditions for modified Mann iteration, Nonlinear Anal., 68 (2008), 1687-1693
##[25]
Y. Yao, Y. J. Cho, Y. C. Liou, Iterative algorithms for hierarchical fixed points problems and variational inequalities, Math. Comput. Modelling, 52 (2010), 1697-1705
##[26]
Y. Yao, Y. J. Cho, Y. C. Liou , Iterative algorithms for variational inclusions, mixed equilibrium problems and fixed point problems approach to optimization problems, Central European J. Math., 9 (2011), 640-656
##[27]
Y. Yao, Y. C. Liou, G. Marino , A hybrid algorithm for pseudo-contractive mappings, Nonlinear Anal., 71 (2009), 4997-5002
##[28]
Y. Yao, M. A. Noor, Y. C. Liou, S. M. Kang, Iterative algorithms for general multivalued variational inequalities, Abstr. Appl. Anal., 2012 (2012), 1-10
##[29]
Y. Yao, M. Postolache, Y. C. Liou, Z. Yao, Construction algorithms for a class of monotone variational inequalities, Optim. Lett., 2015 (2015), 1-10
##[30]
Y. Yao, N, Shahzad, New methods with perturbations for nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2011 (2011), 1-9
##[31]
Y. Yao, N. Shahzad, Y. C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015), 1-15
##[32]
Y. Yao, H. K Xu, Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications, Optim, 60 (2011), 645-658
##[33]
H. Zegeye, N. Shahzad, Viscosity approximation methods for a common fixed point of finite family of nonexpansive mappings, Appl. Math. Comput., 191 (2007), 155-163
]
Approximations for Burgers equations with C-N scheme and RBF collocation methods
Approximations for Burgers equations with C-N scheme and RBF collocation methods
en
en
The Burgers' equation is one of the typical nonlinear evolutionary partial differential equations. In
this paper, a mesh-free method is proposed to solve the Burgers' equation using the finite difference and
collocation methods. With the temporal discretization of the equation using C-N scheme, the solution is
approximated spatially by Radial Basis Function (RBF). The numerical results of two different examples
indicate the high accuracy and
flexibility of the presented method.
3727
3734
Huantian
Xie
School of Science
Linyi University
P. R. China
xiehuantian@163.com
Jianwei
Zhou
School of Science
Linyi University
P. R. China
zhoujianwei@lyu.edu.cn
Ziwu
Jiang
School of Science
Linyi University
P. R. China
jiangziwu@lyu.edu.cn
Xiaoyi
Guo
School of Science
Linyi University
P. R. China
guoxiaoyi@lyu.edu.cn
Burgers' equation
collocation
Crank-Nicholson (C-N) scheme
multiquadric (MQ).
Article.23.pdf
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W. F. Ames, Nonlinear Partial Differential Equations in Engineering, Academic Press, New York-London (1965)
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A. Kurt, Y. Cenesiz, O. Tasbozan, On the solution of Burgers' equation with the new fractional derivative, Open Phys., 13 (2015), 355-360
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L. Xu, J.-H. Zhao, H. Liu, Numerical simulation for the single-bubble electrospinning process, Therm. Sci., 19 (2015), 1255-1259
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X.-J. Yang, J. A. T. Machado, H. M. Srivastava, A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach, Appl. Math. Comput., 274 (2016), 143-151
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X.-J. Yang, H. M. Srivastava, C. Cattani, Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics, Rom. Rep. Phys., 67 (2015), 752-761
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D.-S. Zhang, D.-Z. Pan, H.-Y. Wang, W.-D. Shi, Numerical prediction of cavitating flow around a hydrofoil using pans and improved shear stress transport k-omega model , Therm. Sci., 19 (2015), 1211-1216
]
Some new fixed point theorems in generalized probabilistic metric spaces
Some new fixed point theorems in generalized probabilistic metric spaces
en
en
In this paper, we introduced the notion of \(\alpha-\psi\)-type contractive mapping in PGM-spaces and established
some new fixed point theorems in complete PGM-spaces. Finally, an example is given to support our main
results.
3735
3743
Cuiru
Ji
Department of Mathematics
Nanchang University
P. R. China
cuiruji0809@163.com
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
Zhaoqi
Wu
Department of Mathematics
Nanchang University
P. R. China
PGM-space
\(\alpha-\psi\)-type contractive mapping
\(\phi\)-function
fixed point.
Article.24.pdf
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[1]
S. Banach, Sur les opérations dans les ensemblesn abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133-181
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B. S. Choudhury, K. P. Das, A new contraction principle in Menger spaces, Acta Math. Sin. Engl. Ser., 24 (2008), 1379-1386
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B. S. Choudhury, K. P. Das, A coincidence point result in Menger spaces using a control function, Chaos Solitons Fractals, 42 (2009), 3058-3063
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]
On a solvable for some systems of rational difference equations
On a solvable for some systems of rational difference equations
en
en
In this paper, we study the existence of solutions for a class of rational systems of difference equations
of order four in four-dimensional case
\[x_{n+1} = \frac {x_{n-3}}{\pm 1\pm t_nz_{n-1}y_{n-2}x_{n-3}}, \qquad
y_{n+1} =\frac{ y_{n-3}}
{\pm 1\pm x_nt_{n-1}z_{n-2}y_{n-3}},\]
\[z_{n+1} =\frac{ z_{n-3}}
{\pm 1\pm y_nx_{n-1}t_{n-2}z_{n-3}}, \qquad
t_{n+1} =\frac{ t_{n-3}}
{\pm 1\pm z_ny_{n-1}x_{n-2}t_{n-3}},\]
with the initial conditions are real numbers. Also, we study some behavior such as the periodicity and
boundedness of solutions for such systems. Finally, some numerical examples are given to confirm our
theoretical results and graphed by Matlab.
3744
3759
M. M.
El-Dessoky
Faculty of Science, Mathematics Department
King AbdulAziz University
Saudi Arabia
dessokym@mans.edu.eg
Recursive sequences
difference equation system
periodic solutions.
Article.25.pdf
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Q. Din, T. F. Ibrahim, K. A. Khan, Behavior of a competitive system of second-order difference equations, Sci. World J., 2014 (2014), 1-9
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M. M. El-Dessoky, The form of solutions and periodicity for some systems of third-order rational difference equations, Math. Methods Appl. Sci., 39 (2016), 1076-1092
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M. M. El-Dessoky, E. M. Elsayed, On a solution of system of three fractional difference equations, J. Comput. Anal. Appl., 19 (2015), 760-769
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A. S. Kurbanli, On the behavior of solutions of the system of rational difference equations: \(x_{n+1} = x_{n-1}/x_{n-1}y_{n- 1}; y_{n+1} = y_{n-1}/y_{n-1}x_{n - 1}\); and \(z_{n+1} = x_n/z_{n-1}y_{n - 1}\), Discrete Dyn. Nat. Soc., 2011 (2011), 1-12
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Approximate fixed points of set-valued mapping in b-metric space
Approximate fixed points of set-valued mapping in b-metric space
en
en
We establish existence results related to approximate fixed point property of special types of set-valued
contraction mappings, in the setting of b-metric spaces. As consequences of the main theorem, we give some
fixed point results which generalize and extend various fixed point theorems in the existing literature. A
simple example illustrates the new theory. Finally, we apply our results to establishing the existence of
solution for some differential and integral problems.
3760
3772
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
King Saudi Arabia
bsamet@ksu.edu.sa
Calogero
Vetro
Department of Mathematics and Computer Sciences
University of Palermo
Italy
calogero.vetro@unipa.it
Francesca
Vetro
Department of Energy, Information Engineering and Mathematical Models (DEIM)
University of Palermo
Italy
francesca.vetro@unipa.it
b-metric space
\(\eta\)-contraction
fixed point theorem
integral inclusion.
Article.26.pdf
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A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014), 941-960
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M. Demma, R. Saadati, P. Vetro, Fixed point results on b-metric space via Picard sequences and b-simulation functions, Iran. J. Math. Sci. Inform., 11 (2016), 123-136
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On the convergence and data dependence results for multistep Picard-Mann iteration process in the class of contractive-like operators
On the convergence and data dependence results for multistep Picard-Mann iteration process in the class of contractive-like operators
en
en
In this paper, we introduce a new iteration process and prove the convergence of this iteration process
to a fixed point of contractive-like operators. We also present a data dependence result for such mappings.
Our results unify and extend various results in the existing literature.
3773
3786
Isa
Yildirim
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
isayildirim@atauni.edu.tr
Mujahid
Abbas
Department of Mathematics
Lahore University of Management Sciences
Pakistan
mujahid@lums.edu.pk
Nazli
Karaca
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
nazli.kadioglu@atauni.edu.tr
Fixed point
contractive-like operators
convergence and data dependence.
Article.27.pdf
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[1]
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R. Chugh, V. Kumar, S. Kumar, Stronge converge of a new three step iterative scheme in Banach spaces, Amer. J. Comput. Math., 2 (2012), 345-357
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V. Karakaya, F. Gürsoy, K. Doğan, M. Ertürk, Data dependence results for multistep and CR iterative schemes in the class of contractive-like operators, Abstr. Appl. Anal., 2013 (2013), 1-7
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]
Optimal coincidence points of proximal quasi-contraction mappings in non-Archimedean fuzzy metric spaces
Optimal coincidence points of proximal quasi-contraction mappings in non-Archimedean fuzzy metric spaces
en
en
The aim of this paper is to present fuzzy optimal coincidence point results of fuzzy proximal quasi
contraction and generalized fuzzy proximal quasi contraction of type-1 in the framework of complete non-
Archimedean fuzzy metric space. Some examples are presented to support the results which are obtained
here. These results also hold in fuzzy metric spaces when some mild assumption is added to the set in
the domain of mappings which are involved here. Our results unify, extend and generalize various existing
results in literature.
3787
3801
Zahid
Raza
Department of Mathematics
Department of Mathematics
National University of Computer and Emerging Sciences
University of Sharjah
Pakistan
UAE
zahid.raza@nu.edu.pk;zraza@sharjah.ac.ae
Naeem
Saleem
Department of Mathematics
National University of Computer and Emerging Sciences
Pakistan
naeem.saleem2@gmail.com
Mujahid
Abbas
Department of Mathematics
Department of Mathematics
University of Pretoria
King Abdulaziz University
South Africa
Saudi Arabia
mujahid.abbas@up.ac.za
Fuzzy metric space
fuzzy proximal
quasi contractions
fuzzy expansive mapping
optimal coincidence best proximity point
t-norm.
Article.28.pdf
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[1]
M. Abbas, N. Saleem, M. De la Sen, Optimal coincidence point results in partially ordered non-Archimedean fuzzy metric spaces, Fixed Point Theory Appl., 2016 (2016), 1-44
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S. Chauhan, B. D. Pant, M. Imdad, Coincidence and common fixed point theorems in Non-Archimedean Menger PM-spaces, Cubo, 15 (2013), 31-44
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P. Salimi, C. Vetro, P. Vetro, Some new fixed point results in Non-Archimedean fuzzy metric spaces, Nonlinear Anal. Model. Control, 18 (2013), 344-358
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Positive solutions to a class of q-fractional difference boundary value problems with \(\phi\)-Laplacian operator
Positive solutions to a class of q-fractional difference boundary value problems with \(\phi\)-Laplacian operator
en
en
By virtue of the upper and lower solutions method, as well as the Schauder fixed point theorem, the
existence of positive solutions to a class of q-fractional difference boundary value problems with \(\phi\)-Laplacian
operator is investigated. The conclusions here extend existing results.
3802
3807
Jidong
Zhao
Department of Foundation
Shandong Yingcai University
P. R. China
zhaojidong0914@163.com
Fractional q-difference
\(\phi\)-Laplacian operator
upper and lower solutions method
Schauder fixed point theorem
positive solution.
Article.29.pdf
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[1]
B. Ahmad, J. Nieto, A. Alsaedi, H. Al-Hutami, Existence of solutions for nonlinear fractional q-difference integral equations with two fractional orders and nonlocal four-point boundary conditions, J. Franklin Inst., 351 (2014), 2890-2909
##[2]
R. A. C. Ferreira, Positive solutions for a class of boundary value problems with q-fractional differences, Comput. Math. Appl., 61 (2011), 367-373
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V. Kac, P. Cheungşel, Quantum Calculus, Springer Press, New York (2002)
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F. Miao, S. Liang, Uniqueness of positive solutions for fractional difference boundary-value problems with p- Laplacian operator, Electron. J. Differ. Equ., 2013 (2013), 1-11
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W. Yang, Positive solution for q-fractional difference boundary value problems with \(\phi\)-Laplacian operator, Bull. Malays. Math. Sci. Soc., 36 (2013), 1195-1203
##[6]
L. Yang, H. Chen, L. P. Luo, Z. G. Luo, Successive iteration and positive solutions for boundary value problem of nonlinear q-fractional difference equation, J. Appl. Math. Comput, 42 (2013), 89-102
]
Infinitely Many Radial Solutions for the Fractional Schrodinger-Poisson Systems
Infinitely Many Radial Solutions for the Fractional Schrodinger-Poisson Systems
en
en
In this paper, we study the following fractional Schrödinger-poisson systems involving fractional Laplacian
operator
\[
\begin{cases}
(-\Delta)^s + v(|x|)u + \phi(|x|,u)=f(|x|,u),\,\,\,\,&\ x\in \mathbb{R}^3,\\
(-\Delta)^t \phi = u^2,\,\,\,\,&\ x\in \mathbb{R}^3, \qquad (1)
\end{cases}
\]
where \((-\Delta)^s(s \in (0; 1))\) and \((-\Delta)^t(t \in (0; 1))\) denotes the fractional Laplacian. By variational methods, we
obtain the existence of a sequence of radial solutions.
3808
3821
Huxiao
Luo
School of Mathematics and Statistics
Central South University
P. R. China
wshrm7@126.com
Xianhua
Tang
School of Mathematics and Statistics
Central South University
P. R. China
tangxh@mail.csu.edu.cn
Fractional Schrödinger-poisson systems
radial solution
variational methods.
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A. Ambrosetti, On Schrodinger-Poisson systems, Milan J. Math., 76 (2008), 257-274
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Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities
Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities
en
en
The aim of this paper is to introduce a new class of generalized metric spaces (called RS-spaces) that
unify and extend, at the same time, Branciari’s generalized metric spaces and Jleli and Samet’s generalized
metric spaces. Both families of spaces seen to be different in nature: on the one hand, Branciari’s spaces are
endowed with a rectangular inequality and their metrics are finite valued, but they can contain convergent
sequences with two different limits, or convergent sequences that are not Cauchy; on the other hand, in
Jleli and Samet’s spaces, although the limit of a convergent sequence is unique, they are not endowed with a
triangular inequality and we can found two points at infinite distance. However, we overcome such drawbacks
and we illustrate that many abstract metric spaces (like dislocated metric spaces, b-metric spaces, rectangular
metric spaces, modular metric spaces, among others) can be seen as particular cases of RS-spaces. In order
to show its great applicability, we present some fixed point theorems in the setting of RS-spaces that extend
well-known results in this line of research.
3822
3849
Antonio Francisco Roldan
Lopez de Hierroa
Department of Quantitative Methods for Economics and Business
PAIDI Research Group FQM-268
University of Granada
University of Jaen
Spain
Spain
aroldan@ugr.es;afroldan@ujaen.es
Naseer
Shahzad
Operator Theory and Applications Research Group, Department of Mathematics
King Abdulaziz University
Saudi Arabia
nshahzad@kau.edu.sa
Generalized metric space
Branciari metric space
fixed point
contractive mapping.
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A constraint shifting homotopy method for computing fixed points on nonconvex sets
A constraint shifting homotopy method for computing fixed points on nonconvex sets
en
en
In this paper, a constraint shifting homotopy method for solving fixed point problems on nonconvex sets
is proposed and the existence and global convergence of the smooth homotopy pathways is proved under
some mild conditions. Compared with the previous results, the newly proposed homotopy method requires
that the initial point needs to be only in the shifted feasible set not necessarily in the original feasible
set, which relaxes the condition that the initial point must be an interior feasible point. Some numerical
examples are also given to show the feasibility and effectiveness of our method.
3850
3857
Zhichuan
Zhu
Faculty of Statistics
School of Mathematics and Statistics
Jilin University of Finance and Economics
Northeast Normal University
China
China
zhuzcnh@126.com
Li
Yang
School of Science
Dalian University of Technology
China
yangli96@dlut.edu.cn
Fixed point
self-mapping
homotopy method
nonconvex sets.
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A novel approach to Banach contraction principle in extended quasi-metric spaces
A novel approach to Banach contraction principle in extended quasi-metric spaces
en
en
The purpose of this note is to give a natural approach to the extensions of the Banach contraction
principle in metric spaces endowed with a partial order, a directed graph or a binary relation in terms
of extended quasi-metric. This novel approach is new and may open the door to other new fixed point
theorems. The case of multivalued mappings is also discussed and an analogue result to Nadler's fixed point
theorem in extended quasi-metric spaces is given.
3858
3863
Afrah A. N.
Abdou
Department of Mathematics
King Abdulaziz University
Saudi Arabia
aabdou@kau.edu.sa
Mohammed
Aljohani
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Saudi Arabia
mohaljohani@gmail.com
Mohamed A.
Khamsi
Department of Mathematical Sciences
The University of Texas at El Paso
U.S.A
mohamed@utep.edu
Banach contraction principle
contraction mapping
extended quasi-metric space
fixed point
monotone mapping
multivalued mapping.
Banach contraction principle
contraction mapping
extended quasi-metric space
fixed point
monotone mapping
multivalued mapping.
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Optimality conditions for pessimistic trilevel optimization problem with middle-level problem being pessimistic
Optimality conditions for pessimistic trilevel optimization problem with middle-level problem being pessimistic
en
en
This paper mainly studies the optimality conditions for a class of pessimistic trilevel optimization prob-
lem, of which middle-level is a pessimistic problem. We firstly translate this problem into an auxiliary
pessimistic bilevel optimization problem, by applying KKT approach for the lower level problem. Then we
obtain a necessary optimality condition via the differential calculus of Mordukhovich. Finally, we obtain an
existence theorem of optimal solution by direct method.
3864
3878
Gaoxi
Li
School of Mathematics and Statistics
Wuhan University
P. R. China
gaoxili@whu.edu.cn
Zhongping
Wan
School of Mathematics and Statistics
Computational Science Hubei Key Laboratory
Wuhan University
Wuhan University
P. R. China
P. R. China
mathwanzhp@whu.edu.cn
Jia-Wei
Chen
School of Mathematics and Statistics
Southwest University
P. R. China
J.W.chen713@163.com
Xiaoke
Zhao
School of Mathematics and Statistics
Wuhan University
P. R. China
zhaoxiaokehenan@126.com
Pessimistic trilevel optimization
bilevel programming
optimality conditions.
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]
On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces
On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces
en
en
In the present paper, we generalize the concept of well-posedness to a generalized hemivariational in-
equality, give some metric characterizations of the \(\alpha\)-well-posed generalized hemivariational inequality, and
derive some conditions under which the generalized hemivariational inequality is strongly \(\alpha\)-well-posed in
the generalized sense. Also, we show that the \(\alpha\)-well-posedness of the generalized hemivariational inequality
is equivalent to the \(\alpha\)-well-posedness of the corresponding inclusion problem.
3879
3891
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Information Management
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Cheng Shiu University
Kaohsiung Medical University
Taiwan
Taiwan
simplex_liou@hotmail.com
Ching-Feng
Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Generalized hemivariational inequality
Clarke's generalized directional derivative
well-posedness
inclusion problem.
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Feng-Liu type fixed point results for multivalued mappings on JS-metric spaces
Feng-Liu type fixed point results for multivalued mappings on JS-metric spaces
en
en
In this paper, we present a fixed point theorem for multivalued mappings on generalized metric space in
the sense of Jleli and Samet [M. Jleli, B. Samet, Fixed Point Theory Appl., 2015 (2015), 61 pages]. In fact,
we obtain as a spacial case both b-metric version and dislocated metric version of Feng-Liu's fixed point
result.
3892
3897
Ishak
Altun
College of Science
Department of Mathematics, Faculty of Science and Arts
King Saud University
Kirikkale University
Saudi Arabia
Turkey
ishakaltun@yahoo.com
Nasir Al
Arifi
Geology and Geophysics Department, College of Science
King Saud University
Saudi Arabia
nalarifi@ksu.edu.sa
Mohamed
Jleli
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
Aref
Lashin
Petroleum and Gas Engineering Department, College of Engineering
Faculty of Science, Geology Department
King Saud University
Benha University
Saudi Arabia
Egypt
arlashin@ksu.edu.sa
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Fixed point
multivalued mapping
generalized metric space
b-metric space
dislocated metric space.
Article.36.pdf
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]
On generalized space of quaternions and its application to a class of Mellin transforms
On generalized space of quaternions and its application to a class of Mellin transforms
en
en
The Mellin integral transform is an important tool in mathematics and is closely related to Fourier
and bi-lateral Laplace transforms. In this article we aim to investigate the Mellin transform in a class of
quaternions which are coordinates for rotations and orientations. We consider a set of quaternions as a set
of generalized functions. Then we provide a new definition of the cited Mellin integral on the provided set
of quaternions. The attributive Mellin integral is one-to-one, onto and continuous in the quaternion spaces.
Further properties of the discussed integral are given on a quaternion context.
3898
3908
Shrideh Khalaf Qasem
Al-Omari
Department of Physics and Basic Sciences, Faculty of Engineering Technology
Al-Balqa Applied University
Jordan
s.k.q.alomari@fet.edu.jo
Dumitru
Baleanu
Department of Mathematics
cInstitute of Space Sciences
Cankaya University
Magurele-Bucharest
Turkey
Romania
dumitru@cankaya.edu.tr
Mellin transform
rotations
quaternions
Laplace transform
Boehmians.
Article.37.pdf
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[1]
S. K. Q. Al-Omari , Hartley transforms on certain space of generalized functions, Georgian Math. J., 20 (2013), 415-426
##[2]
S. K. Q. Al-Omari, Some characteristics of S transforms in a class of rapidly decreasing Boehmians, J. Pseudo- Differ. Oper. Appl., 5 (2014), 527-537
##[3]
S. K. Q. Al-Omari , On a class of generalized Meijer-Laplace transforms of Fox function type kernels and their extension to a class of Boehmians, Bull. kore. Math. Soc., 2015 (2015), -
##[4]
S. K. Q. Al-Omari, Natural transform in Boehmian spaces, Nonlinear Stud., 22 (2015), 293-299
##[5]
S. K. Q. Al-Omari, P. Agarwal, Some general properties of a fractional Sumudu transform in the class of Boehmians , Kuwait J. Sci. Eng., 43 (2016), -
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S. K. Q. Al-Omari, D. Baleanu, On the generalized Stieltjes transform of Fox’s kernel function and its properties in the space of generalized functions, J. Comput. Anal. Appl., (in press.), -
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P. K. Banerji, S. K. Q. Al-Omari, L. Debnath, Tempered distributional Fourier sine (cosine) transform, Integral Transforms Spec. Funct., 17 (2006), 759-768
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Regularization iterative algorithms for monotone and strictly pseudocontractive mappings
Regularization iterative algorithms for monotone and strictly pseudocontractive mappings
en
en
In this article, the sum of a monotone mapping, an inverse strongly monotone mapping, and a strictly
pseudocontractive mapping are investigated based on two regularization iterative algorithms. Strong convergence analysis of the two iterative algorithms is obtained in the framework of real Hilbert spaces.
3909
3919
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
South Korea
ooly61@hotmail.com
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Xiaolong
Qin
Institute of Fundamental and Frontier Sciences
University of Electronic Science and Technology of China
P. R. China
qxlxajh@163.com
Monotone mapping
iterative algorithm
zero point
variational inclusion
resolvent technique.
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B. A. Bin Dehaish, X. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
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S. Y. Cho, X. Qin, L. Wang , Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-15
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X. Qin, S. Y. Cho, L. Wang, Convergence of splitting algorithms for the sum of two accretive operators with applications, Fixed Point Theory Appl., 2014 (2014), 1-12
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X. Qin, S. Y. Cho, L. Wang, Iterative algorithms with errors for zero points of m-accretive operators, Fixed Point Theory Appl., 2013 (2013), 1-17
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R. T. Rockfellar, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res., 1 (1976), 97-116
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R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optimization, 14 (1976), 877-898
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T. Suzuki, Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semi- groups without Bochner integrals , J. Math. Anal. Appl., 305 (2005), 227-239
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T. Suzuki , Moudafi's viscosity approximations with Meir-Keeler contractions, J. Math. Anal. Appl., 325 (2005), 342-352
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Z. M. Wang, X. Zhang, Shrinking projection methods for systems of mixed variational inequalities of Browder type, systems of mixed equilibrium problems and fixed point problems, J. Nonlinear Funct. Anal., 214 (2014), 1-15
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L. Yang, F. Zhao, Strong convergence theorems by Halpern-type iterations for relatively nonexpansive multi-valued mappings in Banach spaces, Nonlinear Funct. Anal. Appl., 17 (2012), 433-441
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J. Zhao, S. Wang, Viscosity approximation method for the split common fixed point problem of quasi-strict pseudo- contractions without prior knowledge of operator norms, Noninear Funct. Anal. Appl., 20 (2015), 199-213
]
A new viscosity approximation method for common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in Banach spaces
A new viscosity approximation method for common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in Banach spaces
en
en
By use of a new viscosity approximation method, we construct an explicit iterative algorithm
for finding common fixed points of a sequence of nonexpansive mappings with weakly contractive
mappings in the framework of Banach spaces. A strong convergence theorem is obtained for solving
a kind of variational inequality problems. Our results improve and extend the corresponding ones of
other authors with related interest.
3920
3930
Wei-Qi
Deng
School of Statistics and Mathematics
Yunnan University of Finance and Economics
China
dwq1273@126.com
Viscosity approximation
nonexpansive mappings with weakly contractive mappings
common fixed points
variational inequalities.
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I. Y. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New results in operator theory and its applications, 7-22, Oper. Theory Adv. Appl., 98, Birkhuser, Basel (1997)
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A. Razani, S. Homaeipour , Viscosity approximation to common fixed points of families of nonexpansive mappings with weakly contractive mappings , Fixed Point Theory Appl., 2010 (2010), 1-8
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B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683-2693
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Y. Song, R. Chen, Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces, Nonlinear Anal., 66 (2007), 591-603
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W. Takahashi , Nonlinear functional analysis: fixed point Theory and its applications, Yokohama Pub- lishers, Yokohama (2000)
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S. S. Zhang, X. R. Wang, H. W. J. Lee, C. K. Chan, Viscosity method for hierarchical fixed point and variational inequalities with applications, Appl. Math. Mech. (English Ed.), 32 (2011), 241-250
]
A graphical version of Reichs fixed point theorem
A graphical version of Reichs fixed point theorem
en
en
In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined
in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results
for these mappings. We also introduce a vector valued Bernstein operator on the space C([0; 1];X), where
X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.
3931
3938
Monther R.
Alfuraidan
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Saudi Arabia
monther@kfupm.edu.sa
Mostafa
Bachar
Department of Mathematics, College of Sciences
King Saud University
Saudi Arabia
mbachar@ksu.edu.sa
Mohamed A.
Khamsi
Department of Mathematical Sciences
University of Texas at El Paso
U. S. A.
mohamed@utep.edu
Multivalued monotone contraction
graph theory
fixed point theory
partial order.
Article.40.pdf
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[1]
M. R. Alfuraidan , Remarks on monotone multivalued mappings on a metric space with a graph, J. Inequal. Appl., 2015 (2015), 1-7
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux quations intègrales, Fund. Math., 3 (1922), 133-181
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I. Beg, A. R. Butt, Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699-3704
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H. Busemann, Spaces with non-positive curvature, Acta. Math., 80 (1948), 259-310
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M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc., 12 (1961), 7-10
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Y. Feng, S. Liu, Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl., 317 (2006), 103-112
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K. Goebel, W. A. Kirk , Topics in metric fixed point theory, Cambridge University Press, Cambridge (1990)
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W. A. Kirk, Fixed point theory for nonexpansive mappings, Lecture Notes in Mathematics, Springer, Berlin, (1981), 485-505
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W. A. Kirk, A fixed point theorem in CAT(0) spaces and R-trees, Fixed Point Theory Appl., 2004 (2004), 309-316
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D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139
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L. Leustean, A quadratic rate of asymptotic regularity for CAT (0)-spaces, J. Math. Anal. Appl., 325 (2007), 386-399
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N. Mizoguchi, W. Takahashi, Fixed Point Theorems for Multivalued Mappings on Complete Metric Spaces, J. Math. Anal. Appl., 141 (1989), 177-188
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S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
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S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital., 5 (1972), 26-42
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]
Splitting methods for monotone operators and bifunctions
Splitting methods for monotone operators and bifunctions
en
en
The purpose of this article is to investigate fixed point problems of a nonexpansive mapping, solutions of
quasi variational inclusion problem, and solutions of a generalized equilibrium problem based on a splitting
method. Our convergence theorems are established under mild restrictions imposed on the control sequences.
The main results improve and extend the recent corresponding results.
3939
3947
Yan
Hao
School of Mathematics, Physics and Information Science
Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Zhejiang Ocean University
China
China
zjhaoyan@aliyun.com
Zhisong
Liu
School of Mathematics, Physics and Information Science
Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Zhejiang Ocean University
China
China
Sun Young
Cho
School of Mathematics
Gyeongsang National University
Korea
ooly61@hotmail.com
Variational inclusion
monotone operator
operator equation
bifunction
convergence.
Article.41.pdf
[
[1]
R. P. Agarwal, R. U. Verma, The over-relaxed \(\eta\)-proximal point algorithm and nonlinear variational inclusion problems, Nonlinear Funct. Anal. Appl., 15 (2010), 63-77
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B. A. Bin Dehaish, A. Latif, H. O. Bakodah, X. Qin , A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 1-14
##[3]
B. A. Bin Dehaish, X. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
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E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Stud., 63 (1994), 123-145
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F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Natl. Acad. Sci. USA, 54 (1965), 1041-1044
##[6]
S.-S. Chang, Existence and approximation of solutions of set-valued variational inclusions in Banach spaces, Nonlinear Anal., 47 (2001), 583-594
##[7]
S.-S. Chang, J.-A. Liu, Y. J. Cho, On the iterative approximation problems of fixed points for asymptotically nonexpansive type mappings in Banach spaces, Nonlinear Funct. Anal. Appl., 6 (2001), 257-270
##[8]
S. Y. Cho, X. Qin , On the strong convergence of an iterative process for asymptotically strict pseudocontractions and equilibrium problems, Appl. Math. Comput., 235 (2014), 430-438
##[9]
S. Y. Cho, X. Qin, L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-15
##[10]
S. Y. Cho, X. Qin, S. M. Kang, Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions, Appl. Math. Lett., 25 (2012), 854-857
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J. K. Kim, Convergence theorems of iterative sequences for generalized equilibrium problems involving strictly pseudocontractive mappings in Hilbert spaces , J. Comput. Anal. Appl., 18 (2015), 454-471
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##[14]
M. Liu, S.-S. Chang, An iterative method for equilibrium problems and quasi-variational inclusion problems , Nonlinear Funct. Anal. Appl., 14 (2009), 619-638
##[15]
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Sliding Bifurcation Analysis and Global Dynamics for a Filippov Predator-prey System
Sliding Bifurcation Analysis and Global Dynamics for a Filippov Predator-prey System
en
en
This paper studies a Filippov predator-prey system, where chemical control strategies are proposed
and analyzed. Initially, the exact sliding segment and its domains are addressed. Then the existence and
stability of the regular, virtual, pseudo-equilibria and tangent points are discussed. It shows that two
regular equilibria and a pseudo-equilibrium can coexist. By employing theoretical and numerical techniques
several kinds of bifurcations are investigated, such as sliding bifurcations related to the boundary node
(focus) bifurcations, touching bifurcations, sliding crossing bifurcation and buckling bifurcations (or sliding
switching). Furthermore, it makes comparison of the obtained results with previous studies for the Filippov
predator-prey system without control strategies. Some biological implications of our results with respect to
pest control are also given.
3948
3961
Xuewen
Tan
College of Mathematics and Information Science
School of Mathematics and Computer Science
Shaanxi Normal University
Yunnan Minzu University
P. R. China
P. R. China
tanxw520@163.com
Wenjie
Qin
College of Science
China Three Gorges University
P. R. China
Xinzhi
Liu
Department of Applied Mathematics
University of Waterloo
Canada
Jin
Yang
Department of Mathematics
Chongqing Jiaotong University
P. R. China
Shaoping
Jiang
School of Mathematics and Computer Science
Yunnan Minzu University
P. R. China
Filippov predator-prey system
control strategy
economic threshold
sliding bifurcation analysis.
Article.42.pdf
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]
Common fixed point for three pairs of self-maps satisfying weakly commuting and weakly compatible condition in generalized metric spaces
Common fixed point for three pairs of self-maps satisfying weakly commuting and weakly compatible condition in generalized metric spaces
en
en
In this paper, we use weakly commuting and weakly compatible conditions of self-mapping pairs, prove
some new common fixed point theorems for three pairs of self-maps in the framework of generalized metric
spaces. The results presented in this paper generalize the well known comparable results in the literature
due to Abbas et al. [M. Abbas, T. Nazir, R. Saadati, Adv. Difference Equ., 2011 (2011), 20 pages]. We
also provide illustrative examples in support of our new results.
3962
3979
Zhongzhi
Yang
Accounting School
Zhejiang University of Finance and Economics
China
zzyang_99@163.com
Generalized metric space
weakly commuting mapping pairs
weakly compatible mapping pairs
common fixed point.
Article.43.pdf
[
[1]
M. Abbas, S. H. Khan, T. Nazir , Common fixed points of R-weakly commuting maps in generalized metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-11
##[2]
M. Abbas, A. R. Khan, T. Nazir, Coupled common fixed point results in two generalized metric spaces, Appl. Math. Comput., 217 (2011), 6328-6336
##[3]
M. Abbas, T Nazir, D. Doric, , Common fixed point of mappings satisfying (E:A) property in generalized metric spaces, Appl. Math. Comput, 218 (2012), 7665-7670
##[4]
M. Abbas, T. Nazir, S. Radenovic, Some periodic point results in generalized metric spaces, Appl. Math. Comput., 217 (2010), 4094-4099
##[5]
M. Abbas, T. Nazir, R. Saadati, Common fixed point results for three maps in generalized metric space, Adv. Difference Equ., 2011 (2011), 1-20
##[6]
M. Abbas, T. Nazir, P. Vetro, Common fixed point results for three maps in G-metric spaces, Filomat, 25 (2011), 1-17
##[7]
M. Abbas, B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., 215 (2009), 262-269
##[8]
H. Aydi, A fixed point result involving a generalized weakly contractive condition in G-metric spaces, Bull. Math. Anal. Appl., 3 (2011), 180-188
##[9]
H. Aydi , A common fixed point of integral type contraction in generalized metric spaces, J. Adv. Math. Stud., 5 (2012), 111-117
##[10]
H. Aydi, W. Shatanawi, C. Vetro, On generalized weakly G-contraction mapping in G-metric spaces, Comput. Math. Appl., 62 (2011), 4222-4229
##[11]
R. Chugh, T. Kadian, A. Rani, B. E. Rhoades, Property P in G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-12
##[12]
F. Gu, Common fixed point theorems for six mappings in generalized metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-21
##[13]
F. Gu , Some new common coupled fixed point results in two generalized metric spaces , Fixed Point Theory Appl., 2013 (2013), 1-21
##[14]
F. Gu, W. Shatanawi , Common fixed point for generalized weakly G-contraction mappings satisfying common (E:A) property in G-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-15
##[15]
F. Gu, Z. Yang, Some new common fixed point results for three pairs of mappings in generalized metric spaces , Fixed Point Theory Appl., 2013 (2013), 1-21
##[16]
F. Gu, H. Ye , Common fixed point theorems of Altman integral type mappings in G-metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-13
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F. Gu, Y. Yin, Common fixed point for three pairs of self-maps satisfying common (E:A) property in generalized metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-13
##[18]
F. Gu, Y. Yin, A new common coupled fixed point theorem in generalized metric space and applications to integral equations, Fixed Point Theory Appl., 2013 (2013), 1-16
##[19]
F. Gu, S. Zhou, Coupled common fixed point theorems for a pair of commuting mappings in partially ordered G-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-18
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N. Hussain, E. Karapinar, P. Salimi, P. Vetro, Fixed point results for \(G^m\)-Meir-Keeler contractive and \(G-(\alpha,\psi)\)- Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-14
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N. Hussain, J. R. Roshan, V. Parvaneh, A. Latif, A unification of G-metric, partial metric and b-metric spaces, Abstr. Appl. Anal., 2014 (2014), 1-15
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A. Kaewcharoen, Common fixed point theorems for contractive mappings satisfying \(\Phi\)-maps in G-metric spaces, Banach J. Math. Anal., 6 (2012), 101-111
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A. Kaewcharoen, Common fixed points for four mappings in G-metric spaces, Int. J. Math. Anal., 6 (2012), 2345-2356
##[24]
W. Long, M. Abbas, T. Nazir, S. Radenović, Common fixed point for two pairs of mappings satisfying (E:A) property in generalized metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-15
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S. Manro, S. S. Bhatia, S. Kumar, Expansion mapping theorems in G-metric spaces, Int. J. Contemporary Math. Sci., 5 (2010), 2529-2535
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Z. Mustafa , Common fixed points of weakly compatible mappings in G-metric spaces, Appl. Math. Sci., 6 (2012), 4589-4600
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Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., 2009 (2009), 1-10
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K. P. R. Rao, K. B. Lakshmi, Z. Mustafa, V. C. C. Raju, Fixed and related fixed point theorems for three maps in G-metric spaces, J. Adv. Stud. Topol., 3 (2012), 12-19
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W. Shatanawi, Fixed point theory for contractive mappings satisfying \(\Phi\)-maps in G-metric spaces, Fixed Point Theory Appl., 2010 (2010), 1-9
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S. Shatanawi, Coupled fixed point theorems in generalized metric spaces, Hacet. J. Math. Stat., 40 (2011), 441-447
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W. Shatanawi, M. Abbas, T. Nazir, Common coupled coincidence and coupled fixed point results in two generalized metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-13
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N. Tahat, H. Aydi, E. Karapinar, W. Shatanawi, Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-9
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H. Ye, F. Gu, Common fixed point theorems for a class of twice power type contraction maps in G-metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-19
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Y. Yin, F. Gu , Common fixed point theorem about four mappings in G-metric spaces, J. Hangzhou Norm. Univ. Nat. Sci., 11 (2012), 511-515
]
The stability of quadratic \(\alpha\)-functional equations
The stability of quadratic \(\alpha\)-functional equations
en
en
In this paper, we investigate the quadratic \(\alpha\)-functional equation
\[2f(x) + 2f(y) = f(x - y) + \alpha^{-2}f(\alpha(x + y)); \quad(1)\]
\[2f(x) + 2f(y) = f(x + y) + \alpha^{-2}f(\alpha(x - y));\quad (2)\]
where \(\alpha\) is a fixed nonzero real or complex number with \(\alpha^{-1}\neq \pm\sqrt{3}\).
Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic
\(\alpha\)-functional equations (1) and (2) in Banach spaces.
3980
3991
Sungsik
Yun
Department of Financial Mathematics
Hanshin University
Republic of Korea
ssyun@hs.ac.kr
Choonkill
Park
Research Institute for Natural Sciences
Hanyang University
Republic of Korea
baak@hanyang.ac.kr
Hyers-Ulam stability
quadratic \(\alpha\)-functional equation
fixed point method
direct method
Banach space.
Article.44.pdf
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[1]
T. Aoki , On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
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A. Bahyrycz, M. Piszczek, Hyperstability of the Jensen functional equation, Acta Math. Hungar., 142 (2014), 353-365
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M. Balcerowski, On the functional equations related to a problem of Z. Boros and Z. Daróczy, Acta Math. Hungar., 138 (2013), 329-340
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L. Cadariu, V. Radu , Fixed points and the stability of Jensen's functional equation , J. Inequal. Pure Appl. Math., 4 (2003), 1-7
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Z. Daróczy, Gy. Maksa, A functional equation involving comparable weighted quasi-arithmetic means, Acta Math. Hungar., 138 (2013), 147-155
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V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4 (2003), 91-96
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]
Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions
Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions
en
en
In this paper, we study the existence of positive solutions to the nonlinear fractional order singular and
semipositone nonlocal boundary value problem
\[
\begin{cases}
\mathfrak{D}^\alpha_{0^+}u(t)+f(t,u(t))=0,\,\,\,\,\, 0<t<1,\\
u(0)=u'(0)=...=u^{(n-2)}(0)=0,\,\,\,\,\, u(1)=\mu\int^1_0 u(s)ds.
\end{cases}
\]
by using the Leray-Schauder nonlinear alternative and a fixed-point theorem on cones, where \(0 < \mu <
\alpha; 2 \leq n - 1 < \alpha \leq n, \mathfrak{D}^\alpha_{0^+}\)
is the standard Riemann-Liouville derivative, and f(t; u) is semipositone and
may be singular at u = 0.
3992
4002
Xinan
Hao
School of Mathematical Sciences
Qufu Normal University
P. R. China
haoxinan2004@163.com
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University
P. R. China
Australia
lls@mail.qfnu.edu.cn
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University
Australia
yhwu@maths.curtin.edu.au
Singular fractional differential equation
semipositone
positive solutions
nonlocal boundary conditions.
Article.45.pdf
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[1]
O. P. Agrawal , Formulation of Euler-Lagrange equations for fractional variational problems, J. Math. Anal. Appl., 272 (2002), 368-379
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B. Ahmad, J. J. Nieto, Existence results for higher order fractional differential inclusions with nonlocal boundary conditions , Nonlinear Stud., 17 (2010), 131-138
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C. S. Goodrich, Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions, Comput. Math. Appl., 61 (2011), 191-202
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X. Hao, Positive solution for singular fractional differential equations involving derivatives, Adv. Difference Equ., 2016 (2016), 1-12
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V. Lakshmikantham, A. S. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations , Appl. Math. Lett., 21 (2008), 828-834
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M. ur Rehman, R. A. Khan , Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations, Appl. Math. Lett., 23 (2010), 1038-1044
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X. Xu, X. Fei , The positive properties of Green's function for three point boundary value problems of nonlinear fractional differential equations and its applications, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1555-1565
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X. Xu, D. Jiang, C. Yuan, Multiple positive solutions to singular positone and semipositone Dirichlet-type boundary value problems of nonlinear fractional differential equations, Nonlinear Anal., 74 (2011), 5685-5696
##[18]
C. Yuan , Two positive solutions for (n - 1; 1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations , Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 930-942
##[19]
X. Zhang, L. Liu, Y. Wu, Multiple positive solutions of a singular fractional differential equation with negatively perturbed term, Math. Comput. Modelling, 55 (2012), 1263-1274
##[20]
X. Zhang, L. Liu, Y. Wu , The uniqueness of positive solution for a singular fractional differential system involving derivatives, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 1400-1409
]
On the split equality common fixed point problem for asymptotically nonexpansive semigroups in Banach spaces
On the split equality common fixed point problem for asymptotically nonexpansive semigroups in Banach spaces
en
en
In this article, we propose an iteration methods for finding a split equality common fixed point of
asymptotically nonexpansive semigroups in Banach spaces. The weak and strong convergence theorems of
the iteration scheme proposed are obtained. As application, we shall utilize our results to study the split
equality variational inequality problems to support the main results. The results presented in the article
are new and improve and extend some recent corresponding results.
4003
4015
Zhaoli
Ma
School of Information Engineering, The College of Arts and Sciences
Yunnan Normal University
China
kmszmzl@126.com
Lin
Wang
College of Statistics and Mathematics
Yunnan University of Finance and Economics
China
WL64mail@aliyun.com;Wanglin64@outlook.com
Split equality problem
convergence
asymptotically nonexpansive semigroup
Banach spaces.
Article.46.pdf
[
[1]
H. Attouch, J. Bolte, P. Redont, A. Soubeyran, Alternating proximal algorithms for weakly coupled convex minimization problems, Applications to dynamical games and PDEs., J. Convex Anal., 15 (2008), 485-506
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On strong intuitionistic fuzzy metrics
On strong intuitionistic fuzzy metrics
en
en
In this paper we give some properties of a class of intuitionistic fuzzy metrics which is called strong. This
new class includes the class of stationary intuitionistic fuzzy metrics. So we examine the relationship between
strong intuitionistic fuzzy metric and stationary intuitionistic fuzzy metric.
4016
4038
Hakan
Efe
Department of Mathematics, Faculty of Science
Gazi University Teknikokullar
Turkey
hakanefe@gazi.edu.tr
Ebru
Yigit
Graduate School of Natural and Applied Science
Gazi University Teknikokullar
Turkey
yigittebru@gmail.com
Continuous t-norm
continuous t-conorm
intuitionistic fuzzy metric
strong intuitionistic fuzzy metric
stationary intuitionistic fuzzy metric.
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Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces
Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces
en
en
The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping
in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain
assumptions imposed on the parameters. As applications, we use our main results to solve fixed point
problems of strict pseudocontractions in Hilbert spaces and variational inequality problems in Hilbert spaces.
Finally, we also give one numerical example to support our main results.
4039
4051
Qian
Yan
School of Mathematics Science
Chongqing Normal University
China
qianyanmath@163.com
Gang
Cai
School of Mathematics Science
Chongqing Normal University
China
caigang-aaaa@163.com
Ping
Luo
School of Mathematics Science
Chongqing Normal University
China
lp10@cqnu.edu.cn
Fixed point
generalized implicit rules
generalized contraction
nonexpansive mapping
Banach spaces.
Article.48.pdf
[
[1]
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]
A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions
A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions
en
en
In this paper, we introduce and analyze a hybrid extragradient algorithm for solving bilevel pseudomonotone
variational inequalities with multiple solutions in a real Hilbert space. The proposed algorithm is based
on Korpelevich's extragradient method, Mann's iteration method, hybrid steepest-descent method, and viscosity
approximation method (including Halpern's iteration method). Under mild conditions, the strong
convergence of the iteration sequences generated by the algorithm is derived.
4052
4069
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Information Management
Research Center of Nonlinear Analysis and Optimization and Center for Fundamental Science
Cheng Shiu University
Kaohsiung Medical University
Taiwan
Taiwan
simplex_liou@hotmail.com
Ching-Feng
Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Bilevel variational inequality
hybrid extragradient algorithm
pseudomonotonicity
Lipschitz continuity
global convergence.
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]
Iterative solution for nonlinear impulsive advection- reaction-diffusion equations
Iterative solution for nonlinear impulsive advection- reaction-diffusion equations
en
en
Through solving equations step by step and by using the generalized Banach fixed point theorem, under
simple conditions, the authors present the existence and uniqueness theorem of the iterative solution for
nonlinear advection-reaction-diffusion equations with impulsive effects. An explicit iterative scheme for the
solution is also derived. The results obtained generalize and improve some known results.
4070
4077
Xinan
Hao
School of Mathematical Sciences
Qufu Normal University
P. R. China
haoxinan2004@163.com
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University
P. R. China
Australia
lls@mail.qfnu.edu.cn
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University
Australia
yhwu@maths.curtin.edu.au
Iterative solution
nonlinear advection-reaction-diffusion equations
impulse.
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Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings
Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings
en
en
In this paper, we prove the analog to Browder and Göhde fixed point theorem for \(G\)-nonexpansive
mappings in complete hyperbolic metric spaces uniformly convex. In the linear case, this result is refined.
Indeed, we prove that if X is a Banach space uniformly convex in every direction endowed with a graph \(G\),
then every \(G\)-nonexpansive mapping \(T : A \rightarrow A\), where \(A\) is a nonempty weakly compact convex subset of
\(X\), has a fixed point provided that there exists \(u_0 \in A\) such that \(T(u_0)\) and \(u_0\) are \(G\)-connected.
4078
4083
Monther Rashed
Alfuraidan
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Saudi Arabia
monther@kfupm.edu.sa
Sami Atif
Shukri
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Saudi Arabia
samishukri@kfupm.edu.sa
Directed graph
fixed point
G-nonexpansive mapping
hyperbolic metric space
Mann iteration
uniformly convex space.
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Refinements of Caristis fixed point theorem
Refinements of Caristis fixed point theorem
en
en
In this paper, we introduce new types of Caristi fixed point theorem and Caristi-type cyclic maps in
a metric space with a partial order or a directed graph. These types of mappings are more general than
that of Du and Karapinar [W.-S. Du, E. Karapinar, Fixed Point Theory Appl., 2013 (2013), 13 pages]. We
obtain some fixed point results for such Caristi-type maps and prove some convergence theorems and best
proximity results for such Caristi-type cyclic maps. It should be mentioned that in our results, all the optional
conditions for the dominated functions are presented and discussed to our knowledge, and the replacing of
\(d(x; Tx)\) by \(\min\{d(x; Tx); d(Tx; Ty)\}\) endowed with a graph makes our results strictly more general. Many
recent results involving Caristi fixed point or best proximity point can be deduced immediately from our
theory. Serval applications and examples are presented making effective the new concepts and results. Two
analogues for Banach-type contraction are also provided.
4084
4097
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Dong
Zhang
School of Mathematical Sciences
Peking University
China
dongzhang@pku.edu.cn
Caristi fixed point theorem
cyclic map
Banach fixed point theorem.
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M. R. Alfuraidan, M. A. Khamsi, Caristi fixed point theorem in metric spaces with a graph, Abstr. Appl. Anal., 2014 (2014), 1-5
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]
A note on coincidence points of multivalued weak G-contraction mappings
A note on coincidence points of multivalued weak G-contraction mappings
en
en
In this note, we discuss the definition of the multivalued weak contraction mappings defined in a metric
space endowed with a graph as introduced by Hanjing and Suantai[A. Hanjing, S. Suantai, Fixed Point
Theory Appl., 2015 (2015), 10 pages]. In particular, we show that this definition is not correct and give the
correct definition of the multivalued weak contraction mappings defined in a metric space endowed with a
graph. Then we prove the existence of coincidence points for such mappings.
4098
4103
Monther Rashed
Alfuraidan
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Saudi Arabia
monther@kfupm.edu.sa
Mohamed Amine
Khamsi
Department of Mathematical Sciences
University of Texas at El Paso
U. S. A.
mohamed@utep.edu
Directed graph
coincidence points
weak G-contraction mappings
Reich multivalued mapping.
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[1]
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A. Hanjing, S. Suantai, Coincidence point and fixed point theorems for a new type of G-contraction multivalued mappings on a metric space endowed with a graph, Fixed Point Theory Appl., 2015 (2015), 1-10
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443
]
Existence of solutions and Hadamard well-posedness for generalized strong vector quasi-equilibrium problems
Existence of solutions and Hadamard well-posedness for generalized strong vector quasi-equilibrium problems
en
en
In this paper, we establish an existence result for the (GSVQEP) without assuming that the dual of the
ordering cone has a weak star compact base and give an example to show our existence theorem is different
from the main result of Long et al. [X. J. Long, N. J. Huang, K. L. Teo, Math. Comput. Modelling, 47
(2008), 445-451]. Furthermore, we introduce a concept of Hadamard-type well-posedness for the (GSVQEP)
and establish sufficient conditions of Hadamard-type well-posedness for the (GSVQEP).
4104
4113
Jing
Zeng
College of Mathematics and Statistics
Chongqing Technology and Business University
China
yiyuexue219@163.com
Zai-Yun
Peng
College of Mathematics and Statistics, School of Science
Chongqing Jiaotong University
China
pengzaiyun@126.com
Xiang-Kai
Sun
College of Mathematics and Statistics
Chongqing Technology and Business University
China
sxkcqu@163.com
Xian-Jun
Long
College of Mathematics and Statistics
Chongqing Technology and Business University
China
xianjunlong@hotmail.com
Existence theorem
Hadamard well-posedness
fixed-point theorem
lower semicontinuity
naturally quasi-convexity.
Existence theorem
Hadamard well-posedness
fixed-point theorem
lower semicontinuity
naturally quasi-convexity.
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]
New fixed point results for contractive maps involving dominating auxiliary functions
New fixed point results for contractive maps involving dominating auxiliary functions
en
en
In this paper, we establish certain new fixed point theorems for contractive inequalities using an auxiliary
function which dominates the ordinary metric function. As application, we derive some recent known results
as corollaries. Certain interesting consequences of our results are also presented. An example is given to
illustrate the usability of the obtained results.
4114
4126
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Peyman
Salimi
Young Researchers and Elite Club
Rasht Branch, Islamic Azad University
Iran
salimipeyman@gmail.com
Triangular \(\alpha\)-admissible mapping
F-contraction
indirected metric space.
Article.55.pdf
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[1]
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Md. Ahmadullah, J. Ali, M. Imdad , Unified relation-theoretic metrical fixed point theorems under an implicit contractive condition with an application, Fixed Point Theory Appl., 2016 (2016), 1-15
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N. Hussain, D. Doric, Z. Kadelburg, S. Radenovic, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 1-12
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N. Hussain, A. Latif, I. Iqbal, Fixed point results for generalized F-contractions in modular metric and fuzzy metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-20
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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T. Suzuki , A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317
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T. Suzuki , A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869
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D. Wardowski , Fixed points of a new type of contractive mappings in complete metric spaces , Fixed Point Theory Appl., 2012 (2012), 1-6
]
Some fixed point theorems concerning (\(\psi,\phi\))-type contraction in complete metric spaces
Some fixed point theorems concerning (\(\psi,\phi\))-type contraction in complete metric spaces
en
en
The purpose of this paper is to introduce the notions of (\(\psi,\phi\))-type contractions and (\(\psi,\phi\))-type Suzuki
contractions and to establish some new fixed point theorems for such kind of mappings in the setting of
complete metric spaces. The results presented in the paper are an extension of the Banach contraction
principle, Suzuki contraction theorem, Jleli and Samet fixed point theorem, Piri and Kumam fixed point
theorem.
4127
4136
Xin-Dong
Liu
Department of Mathematics
Yibin University
China
Shih-Sen
Chang
Center for General Education
China Medical University
Taiwan
changss12013@163.com
Yun
Xiao
Department of Mathematics
Yibin University
China
Liang-Cai
Zhao
Department of Mathematics
Yibin University
China
Contraction principle
fixed point
(\(\psi،\phi\))-type contraction
( \(\psi،\phi\))-type Suzuki contraction.
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M. Jleli, E. Karapınar, B. Samet , Further generalizations of the Banach contraction principle , J. Inequal. Appl., 2014 (2014), 1-9
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M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
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]
A general iterative algorithm for common solutions of quasi variational inclusion and fixed point problems
A general iterative algorithm for common solutions of quasi variational inclusion and fixed point problems
en
en
In this paper, quasi-variational inclusion and fixed point problems are investigated based on a general
iterative process. Strong convergence theorems are established in the framework of Hilbert spaces.
4137
4147
Xiangsong
Meng
Department of Economic Management
North China Electric Power University
China
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
Korea
ooly61@hotmail.com
Xiaolong
Qin
Institute of Fundamental and Frontier Sciences
University of Electronic Science and Technology of China
China
qxlxajh@163.com
Monotone operator
quasi-variational inclusion
nonexpansive mapping
convex optimization
Hilbert space.
Article.57.pdf
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R. U. Verma, New approach to the \(\eta\)-proximal point algorithm and nonlinear variational inclusion problems, Appl. Math. Comput., 217 (2010), 3155-3165
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Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints
Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints
en
en
In this paper, we introduce and analyze a multi-step hybrid steepest-descent algorithm by combining Korpelevich's
extragradient method, viscosity approximation method, hybrid steepest-descent method, Mann's
iteration method and gradient-projection method (GPM) with regularization in the setting of infinite-dimensional
Hilbert spaces. Strong convergence was established.
4148
4166
L. C.
Ceng
Department of Mathematics
Shanghai Normal University
P. R. China
zenglc@hotmail.com
Y. C.
Liou
Department of Healthcare Administration and Medical Informatics
Kaohsiung Medical University
Taiwan
simplex_liou@hotmail.com
D. R.
Sahu
Department of Mathematics, Institute of Science
Banaras Hindu University
India
drsahudr@gmail.com
Hybrid steepest-descent method
split feasibility problem
generalized mixed equilibrium problem
variational inclusion
maximal monotone mapping
nonexpansive mapping.
Article.58.pdf
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L. C. Ceng, S. M. Guu, J. C. Yao, Hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems, Fixed Point Theory Appl., 2012 (2012), 1-19
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L. C. Ceng, M. M. Wong, A. Petrusel, J. C. Yao , Relaxed implicit extragradient-like methods for finding minimum- norm solutions of the split feasibility problem , Fixed Point Theory, 14 (2013), 327-344
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L. C. Ceng, J. C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math., 214 (2008), 186-201
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L. C. Ceng, J. C. Yao, Relaxed and hybrid viscosity methods for general system of variational inequalities with split feasibility problem constraint, Fixed Point Theory App., 2013 (2013), 1-50
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J. W. Peng, J. C. Yao , A new hybrid-extragradient method for generalized mixed equilibrium problems, fixed point problems and variational inequality problems, Taiwanese J. Math., 12 (2008), 1401-1432
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]
Stability of weighted Nash equilibrium for multiobjective population games
Stability of weighted Nash equilibrium for multiobjective population games
en
en
This paper studies the existence and stability of weighted Nash equilibria for multiobjective population
games. By constructing a Nash's mapping, the existence of weighted Nash equilibria is established.
Furthermore, via the generic continuity method, each weighted Nash equilibrium is shown to be stable for
most of multiobjective population games when weight combinations and payoff functions are simultaneously
perturbed. Besides, this leads to the stability of Nash equilibria for classical population games with the
perturbed payoff functions. These results play cornerstone role in the research concerning multiobjective
population games.
4167
4176
Guanghui
Yang
School of Mathematics and Statistics
Guizhou University
P. R. China
ghuiyang@126.com
Hui
Yang
School of Mathematics and Statistics
Guizhou University
P. R. China
hui-yang@163.com
Qiqing
Song
School of Science
School of Mathematics and Statistics
Guilin University of Technology
Guizhou University
P. R. China
P. R. China
songqiqing@126.com
Multiobjective population game
weighted Nash equilibrium
stability.
Article.59.pdf
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]
\(C\)-class functions and fixed point theorems for generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings in \(\alpha-\eta-\)complete metric spaces
\(C\)-class functions and fixed point theorems for generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings in \(\alpha-\eta-\)complete metric spaces
en
en
In this paper, we introduce the concept of generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings where \(\psi\) is
the altering distance function and \(\varphi\) is the ultra altering distance function. The unique fixed point theorems
for such mappings in the setting of \(\alpha-\eta-\)-complete metric spaces are proven. We also assure the fixed point
theorems in partially ordered metric spaces. Moreover, the solution of the integral equation is obtained
using our main result.
4177
4190
Arslan Hojat
Ansari
Department of Mathematics
Karaj Branch, Islamic Azad University
Iran
analsisamirmath2@gmail.com
Anchalee
Kaewcharoen
Research Center for Academic Excellence in Mathematics, Department of Mathematics, Faculty of Science
Naresuan University
Thailand
anchaleeka@nu.ac.th
\(\alpha-\eta-\)complete metric spaces
\(\alpha-\eta-\)continuous mappings
triangular \(\alpha\)-orbital admissible mappings with respect to \(\eta\)
C-class functions
generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings.
Article.60.pdf
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[1]
A. H. Ansari , Note on \(\varphi-\psi\)-contractive type mappings and related fixed point, The 2nd Regional Conf. Math. Appl., PNU, (2014), 377-380
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P. Chuadchawna, A. Kaewcharoen, S. Plubtieng, Fixed point theorems for generalized \(\alpha-\eta-\psi\)-Geraghty contraction type mappings in \(\alpha-\eta\)-complete metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 471-485
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]
Stability analysis of epidemic models of Ebola hemorrhagic fever with non-linear transmission
Stability analysis of epidemic models of Ebola hemorrhagic fever with non-linear transmission
en
en
Some Epidemic models with fractional derivatives were proved to be well-defined, well-posed and more
accurate (Brockmann et al. [D. Brockmann, L. Hufnagel, Phys. Review Lett., 98 (2007), 17-27]; Doungmo
Goufo et al. [E. F. Doungmo Goufo, R. Maritz, J. Munganga, Adv. Diff. Equ., 2014 (2014), 9 pages];
Pooseh et al. [S. Pooseh, H. S. Rodrigues, D. F. M. Torres, In: Numerical Analysis and Applied Mathematics, ICNAAM, American Institute of Physics, Melville, (2011), 739-742]), compared to models with the
conventional derivative. In this paper, an Ebola epidemic model with non linear transmission is analyzed.
The model is expressed with the conventional time derivative with a new parameter included, which happens
to be fractional. We proved that the model is well-defined, well-posed. Moreover, conditions for boundedness and dissipativity of the trajectories are established. Exploiting the generalized Routh-Hurwitz Criteria,
existence and stability analysis of equilibrium points for Ebola model are performed to show that they are
strongly dependent on the non-linear transmission. In particular, conditions for existence and stability of
a unique endemic equilibrium to the Ebola system are given. Finally, numerical simulations are provided
for particular expressions of the non-linear transmission (with parameters \(\kappa = 0:01, \kappa = 1\) and \(p = 2\)).
The obtained simulations are in concordance with the usual threshold behavior. The results obtained here
are significant for the fight and prevention against Ebola haemorrhagic fever that has so far exterminated
hundreds of families and is still infecting many people in West-Africa.
4191
4205
Emile Franc Doungmo
Goufo
Department of Mathematical Sciences
University of South Africa, Florida Sciences Campus
003 South Africa
dgoufef@unisa.ac.za
Morgan Kamga
Pene
Department of Mathematical Sciences
University of South Africa, Florida Sciences Campus
003 South Africa
Stella
Mugisha
Department of Mathematical Sciences
University of South Africa, Florida Sciences Campus
003 South Africa
Conventional derivative with a new parameter
Ebola epidemic model
non-linear incidence
existence
stability.
Article.61.pdf
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Almost Kenmotsu \(3-h\)-manifolds with cyclic-parallel Ricci tensor
Almost Kenmotsu \(3-h\)-manifolds with cyclic-parallel Ricci tensor
en
en
In this paper, we prove that the Ricci tensor of an almost Kenmotsu 3-h-manifold is cyclic-parallel if
and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space \(\mathbb{H}^3(-1) \)
or the Riemannian product \(\mathbb{H}^2(-4) \times \mathbb{R}\).
4206
4213
Wenjie
Wang
Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Sciences
Henan Normal University
P. R. China
wangwj072@163.com
Almost Kenmotsu 3-manifold
almost contact metric manifold
Einstein-like metric
cyclic-parallel Ricci tensor.
Article.62.pdf
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Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem
Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem
en
en
In this paper, we introduce two iterative algorithms based on the hybrid steepest descent method for
solving the split feasibility problem. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a solution of the split feasibility problem, which is a solution of a certain
variational inequality. In particular, the minimum norm solution of the split feasibility problem is obtained.
4214
4225
Jong Soo
Jung
Department of Mathematics
Dong-A University
Korea
jungjs@dau.ac.kr
Split feasibility problem
nonexpansive mapping
variational inequality
minimum-norm
projection
bounded linear operator
\(\rho\)-Lipschitzian
\(\eta\)-strongly monotone operator.
Article.63.pdf
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F. Wang, H.-K. Xu, Approximating curve and strong convergence of the CQ algorithms for the split feasibility problem , J. Inequal. Appl., 2010 (2010), 1-13
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H.-K. Xu , A variable Krasnoselskii-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22 (2006), 2021-2034
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Q. Yang, The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems, 20 (2004), 1261-1266
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Y. Yao, P.-X. Yang, S. M. Kang, Composite projection algorithms for the split feasibility problem, Math. Comput. Modeling, 57 (2013), 693-700
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J. Zhao, Q. Yang, Several solution methods for the split feasibility problem, Inverse Problems, 21 (2005), 1791-1799
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General mixed width-integral of convex bodies
General mixed width-integral of convex bodies
en
en
In this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish
some of its inequalities, such as isoperimetric inequality, Aleksandrov-Fenchel inequality, and cyclic inequality.
We also consider the general width-integral of order i and show its related properties and inequalities.
4226
4234
Yibin
Feng
School of Mathematics and Statistics
Hexi University
China
fengyibin001@163.com
General mixed width-integral
mixed width-integral
general width-integral of order i.
Article.64.pdf
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]
On hybrid Caputo fractional integro-differential inclusions with nonlocal conditions
On hybrid Caputo fractional integro-differential inclusions with nonlocal conditions
en
en
We investigate the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential inclusions. A hybrid fixed point theorem of Schaefer type for a sum of three
operators due to Dhage is applied to obtain the main result. The paper concludes with an illustrative
example.
4235
4246
Bashir
Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
bashirahmad_qau@yahoo.com
Sotiris K.
Ntouyas
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
Department of Mathematics
King Abdulaziz University
University of Ioannina
Saudi Arabia
Greece
sntouyas@uoi.gr
Jessada
Tariboon
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Thailand
jessada.t@sci.kmutnb.ac.th
Caputo fractional derivative
integro-differential inclusion
hybrid boundary value problem
fixed point theorem.
Article.65.pdf
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[1]
B. Ahmad, Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations , Appl. Math. Lett., 23 (2010), 390-394
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B. Ahmad, S. K. Ntouyas , A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order, Electron. J. Qual. Theory Differ. Equ., 2011 (2011), 1-15
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B. Ahmad, S. K. Ntouyas , Nonlocal fractional boundary value problems with slit-strips boundary conditions , Fract. Calc. Appl. Anal., 18 (2015), 261-280
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]
The Lie derivative of normal connections
The Lie derivative of normal connections
en
en
In this paper, we state the Lie derivative of normal connection on a submanifold M of the Riemannian
manifold \(\widetilde{M}\). By this vein, we introduce the Lie derivative of the normal curvature tensor on \(M\) and give
some relations between the normal curvature tensor on \(M\) and curvature tensor on \(\widetilde{M}\) in the sense of the
Lie derivative of normal connection. As an application, we give some detailed description of the normal
curvature tensor on \(M\) whether \(M\) is a hypersubface.
4247
4256
Bui Cao
Van
Department of Mathematics
Vinh University
Vietnam
buicaovan@gmail.com
Lie derivative
normal connection
normal curvature.
Article.66.pdf
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K. P. Chi, N. H. Quang, B. C. Van, The Lie derivative of currents on Lie group, Lobachevskii J. Math., 33 (2012), 10-21
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]
Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis
Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis
en
en
The spectral analysis of matrix-valued difference equations of second order having polynomial-type Jost
solutions, was first used by Aygar and Bairamov. They investigated this problem on semi-axis. The main aim
of this paper is to extend similar results to the whole axis. We find polynomial-type Jost solutions of a second
order matrix selfadjoint difference equation to the whole axis. Then, we obtain the analytical properties
and asymptotic behaviors of these Jost solutions. Furthermore, we investigate continuous spectrum and
eigenvalues of the operator \(L\) generated by a matrix-valued difference expression of second order. Finally,
we get that the operator \(L\) has a finite number of real eigenvalues.
4257
4262
Elgiz
Bairamov
Faculty of Science, Department of Mathematics
University of Ankara
Turkey
bairamov.science.ankara.edu.tr
Yelda
Aygar
Faculty of Science, Department of Mathematics
University of Ankara
Turkey
yaygar@science.ankara.edu.tr
Serifenur
Cebesoy
Faculty of Science, Department of Mathematics
University of Ankara
Turkey
scebesoy@ankara.edu.tr
Difference equations
discrete operator
Jost solution
eigenvalue
continuous spectrum.
Article.67.pdf
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M. Adıvar, E. Bairamov, Spectral properties of non-selfadjoint difference operators, J. Math. Anal. Appl., 261 (2001), 461-478
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Menger probabilistic G-metric-like space and fixed point theorems
Menger probabilistic G-metric-like space and fixed point theorems
en
en
In this paper, we first introduce a concept called Menger probabilistic G-metric-like space which is a
generalization of Menger probabilistic metric-like space of Hierro and Sen. Some fixed point theorems for
various kinds of contractions in framework of this space are given. Our results extend some recent ones of
Zhou et al., Hua et al. and Alsulami et al.. Finally, an example is given to illustrate the main result of this
paper.
4263
4276
Yanxia
Lu
Department of Mathematics and physics
North China Electric Power University
China
yanxialuncepu@163.com
Xiaoying
Gong
Department of Mathematics and Sciences
Shijiazhuang University of Economics
China
xiaoyinggonghebei@hotmail.com
Xiaomin
Xu
School of Economics and Management
North China Electric Power University
China
xiaominxuncepu@163.com
Menger space
fixed point
\(\varphi\)-contraction
metric-like space.
Article.68.pdf
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H. C. Hua, M. J. Chen, S. H. Wang , New result on fixed point theorems for \(\varphi\)-contractions in Menger spaces, Fixed Point Theory Appl., 2015 (2015), 1-9
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C. L. Zhou, S. H. Wang, Lj. Ciric, S. M. Alsulami, Generalized probabilistic metric spaces and fixed point thoerems, Fixed Point Theory Appl., 2014 (2014), 1-15
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Fixed point theorems on generalized metric space endowed with graph
Fixed point theorems on generalized metric space endowed with graph
en
en
In this paper, we prove some fixed point theorems for mappings of generalized metric space endowed
with graph. We also construct examples to support our results.
4277
4285
Tayyab
Kamran
Department of Mathematics
Quaid-i-Azam University
Pakistan
tayyabkamran@gmail.com
Mihai
Postolache
Department of Mathematics and Informatics
University Politehnica of Bucharest
Romania
emscolar@yahoo.com
Fahim
Uddin
Department of Mathematics
Center for Advanced Studies in Engineering (CASE)
Quaid-i-Azam University
Pakistan
Pakistan
fahamiiu@gmail.com
Muhammad Usman
Ali
Department of Sciences and Humanities
National University of Computer and Emerging Sciences (FAST)
Pakistan
muh_usman_ali@yahoo.com
Generalized metric space
G-Contraction
G-continuity.
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Caustics of de Sitter spacelike curves in Minkowski 3-space
Caustics of de Sitter spacelike curves in Minkowski 3-space
en
en
In this paper, we consider evolutes of spacelike curves in de Sitter 2-space. Applying the theory of
singularity theory, we find that these evolutes can be seen as one dimensional caustics which are locally
diffeomorphic to lines or ordinary cusps. We establish the relationships between singularities of caustics and
geometric invariants of curves under the action of the Lorentz group.
4286
4294
Jiajing
Miao
School of Mathematics
Mudanjiang Normal University
P. R. China
jiajing0407@126.com
Haiming
Liu
School of Mathematics
Mudanjiang Normal University
P. R. China
liuhm468@nenu.edu.cn
De Sitter 2-space
caustics
singularity theory.
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Existence of nontrivial solutions for a nonlinear fourth-order boundary value problem via iterative method
Existence of nontrivial solutions for a nonlinear fourth-order boundary value problem via iterative method
en
en
In this article, we study a nonlinear fourth-order differential equation two-point boundary value problem.
We use monotone iterative technique and lower and upper solutions of completely continuous operators
to get the existence of nontrivial solutions for the problem. The results can guarantee the existence of
nontrivial sign-changing solutions and positive solutions, and we can construct two iterative sequences for
approximating them. Finally, two examples are given to illustrate the main results.
4295
4304
Chengbo
Zhai
School of Mathematical Sciences
Shanxi University
P. R. China
cbzhai@sxu.edu.cn
Chunrong
Jiang
School of Mathematical Sciences
Shanxi University
P. R. China
1252614741@qq.com
Existence of solutions
fourth-order boundary value problem
iterative method
lower and upper solutions.
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]
Generalizations of Hermite--Hadamard type inequalities for MT-convex functions
Generalizations of Hermite--Hadamard type inequalities for MT-convex functions
en
en
In this paper, we discover two novel integral identities for twice differentiable functions. Under the utility
of these identities, we establish some generalized inequalities for classical integrals and Riemann-Liouville
fractional integrals of the Hermite-Hadamard type via functions whose derivatives absolute values are MTconvex.
At the end, we present applications for special means and several error approximations for the
trapezoidal formula.
4305
4316
Yu-Ming
Chu
School of Mathematics and Computation Science
Hunan City University
China
chuyuming2005@126.com
Muhammad Adil
Khan
Department of Mathematics
University of Peshawar
Pakistan
adilswati@gmail.com
Tahir Ullah
Khan
Department of Mathematics
University of Peshawar
Pakistan
tahirullah348@gmail.com
Tahir
Ali
Department of Mathematics
University of Peshawar
Pakistan
atahir623@gamil.com
MT-convex function
Hermite-Hadamard inequality
fractional integrals
trapezoidal formula
error approximation.
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Proximal Point Algorithms Involving Cesàro Type Mean of Asymptotically Nonexpansive Mappings in CAT(0) Spaces
Proximal Point Algorithms Involving Cesàro Type Mean of Asymptotically Nonexpansive Mappings in CAT(0) Spaces
en
en
In this paper, a new modified proximal point algorithm involving fixed point of Cesàro type mean of
asymptotically nonexpansive mappings in CAT(0) spaces is proposed. We also introduce a new iterative
scheme. Under suitable conditions, the \(\Delta\)-convergence and the strong convergence to a common element
of the set of minimizers of a convex function and the set of fixed points of the Cesàro type mean of
asymptotically nonexpansive mapping in CAT(0) space are proved. The results presented in the paper are
new.
4317
4328
Shih-Sen
Chang
Center for General Educatin
China Medical University
Taiwan
changss2013@163.com
Ching-Feng
Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Jen-Chih
Yao
Center for General Educatin
Research Center for Nonlinear Analysis and Optimization
China Medical University
Kaohsiung Medical University
Taiwan
Taiwan
yaojc@mail.cmu.edu.tw
Convex minimization problem
resolvent identity
CAT(0) space
proximal point algorithm
asymptotically nonexpansive mapping.
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]
Uncountably many solutions of a third order nonlinear difference equation with neutral delay
Uncountably many solutions of a third order nonlinear difference equation with neutral delay
en
en
In this paper, by using the Schauder fixed point theorem, Krasnoselskii fixed point theorem and some
new techniques, we obtain the existence of uncountably many solutions for a third order nonlinear difference
equation with neutral delay of the form
\[\Delta(a(n; x_{a_{1n}}; x_{a_{2n}};... ; x_{a_{rn}})\Delta^2(x_n + b_nx_{n-\tau})+ \Delta h(n; x_{h_{1n}}; x_{h_{2n}}; ... ; x_{h_{kn}})
+ f(n; x_{f_{1n}}; x_{f_{2n}};... ; x_{f_{kn}})
= c_n, n \geq n_0,\]
The results presented improve and generalize some results in literatures. Seven examples are given to
illustrate the results presented in this paper.
4329
4354
Zeqing
Liu
Department of Mathematics
Liaoning Normal University Dalian
People's Republic of China
zeqingliu@163.com
Xiaoying
Zhang
Department of Mathematics
Liaoning Normal University Dalian, , .
People's Republic of China
xiaoyingzhang01@163.com
Jeong Sheok
Ume
Department of Mathematics
Changwon National University
Korea
jsume@changwon.ac.kr
Shin Min
Kang
Department of Mathematics and the Research Institute of Natural Science
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Third order nonlinear difference equation with neutral delay
uncountably many solutions
Schauder fixed point theorem
Krasnoselskii fixed point theorem.
Article.74.pdf
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[1]
R. P. Agarwal, S. R. Grace, Oscillation of certain third-Order difference equations , Comput. Math. Appl., 42 (2001), 379-384
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R. P. Agarwal, J. Henderson, Positive solutions and nonlinear eigenvalue problems for third-Order difference equations, Comput. Math. Appl., 36 (1998), 347-355
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L. H. Erbe, Q. K. Kong, B. G. Zhang, Oscillatory theorem for functional differential equations, Dekker, (1995)
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L. J. Kong, Q. K. Kong, B. G. Zhang, Positive solutions of boundary value problems for third-order functional difference equations , Comput. Math. Appl., 44 (2002), 481-489
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W. Lu, W. G. Ge, Z. H. Zhao, Oscillatory criteria for third-order nonlinear difference equation with impulses , Comput. Math. Appl., 234 (2010), 3366-3372
##[8]
Z. Liu, M. Jia, S. M. Kang, Y. C. Kwun , Bounded positive solutions for a third order discrete equation, Abst. Appl. Anal., 2012 (2012), 1-12
##[9]
Z. Liu, Y. Lu, S. M. Kang, Y. C. Kwun, Positive solutions and Mann iterative algorithms for a nonlinear three- dimensional difference system, Abst. Appl. Anal., 2014 (2014), 1-23
##[10]
Z. Liu, W. Sun, J. S. Ume, S. M. Kang, Positive solutions of a second order nonlinear neutral delay difference equation, Abst. Appl. Anal., 2012 (2012), 1-30
##[11]
Z. Liu, Y. G. Xu, S. M. Kang , Bounded oscillation criteria for certain third order nonlinear difference equations with several delays and advances, Comput. Math. Appl., 61 (2011), 1145-1161
##[12]
Z. Liu, X. P. Zhang, S. M. Kang, Y. C. Kwun , On positive solutions of a fourth order nonlinear neutral delay difference equation, Abst. Appl. Anal., 2014 (2014), 1-29
##[13]
Z. Liu, L. S. Zhao, J. S. Ume, S. M. Kang, Solvability of a second order nonlinear neutral delay difference equation, Abst. Appl. Anal., 2011 (2011), 1-24
##[14]
N. Parhi , Non-oscillation of solutions of difference equations of third order , Comput. Math. Appl., 62 (2011), 3812-3820
##[15]
N. Parhi, A. Panda , Nonoscillation and oscillation of solutions of a class of third order difference equations, J. Math. Anal. Appl., 336 (2007), 213-223
##[16]
J. Yan, B. Liu , Asymptotic behavior of a nonlinear delay difference equation , Appl. Math. Lett., 8 (1995), 1-1
]
A numerical approximation with IPSUPG algorithm for P-T-T viscoelastic flows
A numerical approximation with IPSUPG algorithm for P-T-T viscoelastic flows
en
en
A numerical approximation for Phan-Thien-Tanner(P-T-T) viscoelastic
flow problems has investigated.
The approximation is proposed by an interior penalty(IP) method and a Streamline Upwind Petrov-
Galerkin(SUPG) method. Meanwhile, the error estimates for the above numerical approximation of the
P-T-T model is derived. The numerical results support the efficiency of the algorithm.
4355
4363
Lei
Hou
Department of Mathematics
Shanghai University
China
houlei@shu.edu.cn
Yunqing
Feng
Department of Mathematics
Shanghai University
China
minervafyq@shu.edu.cn
Lin
Qiu
Department of Mathematics
Shanghai Jiaotong University, Shanghai 200240, China.
China
linqiu@sjtu.edu.cn
Viscoelastic flows
P-T-T model
finite element method
stokes
constitutive equation.
Article.75.pdf
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[1]
J. Baranger, D. Sandri , Finite element approximation of viscoelastic fluid flow: Existence of approximate solutions and error bounds, Numer. Math., 63 (1992), 13-27
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A. Bonito, E. Burman , A Face Penalty Method for the Three Fields Stokes Equation Arising from Oldroyd-B Viscoelastic Flows, Springer, Berlin, (2006), 487-494
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A. Bonito, E. Burman, A Continuous Interior Penalty Method for Viscoelastic Flows, SIAM J. Sci. Comput., 30 (2008), 1156-1177
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V. J. Ervin, W. W. Miles , Approximation of Time-Dependent Viscoelastic Fluid Flow: SUPG Approximation, SIAM J. Numer. Anal., 41 (2003), 457-486
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Y. He, Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations, Math. Comput., 74 (2005), 1201-1216
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Y. Mu, G. Zhao, X. Wu, J. Zhai , Modeling and simulation of three-dimensional planar contraction flow of viscoelastic fluids with PTT, Giesekus and FENE-P constitutive models, Appl. Math. Comput., 218 (2012), 8429-8443
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L. Nadau, A. Sequeira, Numerical simulations of shear dependent viscoelastic flows with a combined finite element and finite volume method , Comput. Math. Appl., 53 (2007), 547-568
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J. Sun, N. Phan-Thien, R. I. Tanner , An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG, J. Non-Newtonian Fluid Mech., 65 (1996), 75-91
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S. Zhou, L. Hou , Decoupled algorithm for solving Phan-Thien-Tanner viscoelastic fluid by finite element method, Comput. Math. Appl., 69 (2015), 423-437
]
The multi-\(\mathbb{F}\)-sensitivity and \((\mathbb{F}_1, \mathbb{F}_2)\)-sensitivity for product systems
The multi-\(\mathbb{F}\)-sensitivity and \((\mathbb{F}_1, \mathbb{F}_2)\)-sensitivity for product systems
en
en
In this paper, it is proved that the product system \((X \times Y; T \times S)\) is multi-\(\mathbb{F}\)-sensitive (resp., \((\mathbb{F}_1, \mathbb{F}_2)\)-
sensitive) if and only if \((X; T)\) or \((Y; S)\) is multi-F-sensitive (resp., \((\mathbb{F}_1, \mathbb{F}_2)\)-sensitive) when Furstehberg
families \(\mathbb{F}\) and \(\mathbb{F}_2\) have the Ramsey property, improving the main results in [N. Değirmenci, Ş. Koçak,
Turk. J. Math., 34 (2010), 593-600] and [R. Li, X. Zhou, Turk. J. Math., 37 (2013), 665-675]. Moreover,
some analogical results for semi-
flows are obtained.
4364
4370
Xinxing
Wu
School of Sciences
Southwest Petroleum University
P. R. China
wuxinxing5201314@163.com
Risong
Li
School of Science
Guangdong Ocean University
P. R. China
gdoulrs@163.com
Yiran
Zhang
School of Electronic Engineering
University of Electronic Science and Technology of China
P. R. China
Multi-\(\mathbb{F}\)-sensitivity
\((\mathbb{F}_1، \mathbb{F}_2)\)-sensitivity
Li-Yorke sensitivity
product system.
Article.76.pdf
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R. Li, Y. Shi , Several sufficient conditions for sensitive dependence on initial conditions, Nonlinear Anal., 72 (2010), 2716-2720
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R. Li, X. Zhou, A note on chaos in product maps, Turk. J. Math., 37 (2013), 665-675
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F. Tan, R. Zhang , On F-sensitive pairs, Acta Math. Sci., 31 (2011), 1425-1435
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X. Ye, R. Zhang , On sensitive sets in topological dynamics, Nonlinearity, 21 (2008), 1601-1620
]
Variations on strong lacunary quasi-Cauchy sequences
Variations on strong lacunary quasi-Cauchy sequences
en
en
We introduce a new function space, namely the space of \(N^\alpha_\theta(p)\)-ward continuous functions, which turns
out to be a closed subspace of the space of continuous functions. A real valued function f defined on a subset
\(A\) of \(\mathbb{R}\), the set of real numbers, is
\(N^\alpha_\theta(p)\)-ward continuous if it preserves
\(N^\alpha_\theta(p)\)-quasi-Cauchy sequences,
that is, \((f(x_n))\) is an
\(N^\alpha_\theta(p)\)-quasi-Cauchy sequence whenever \((x_n)\) is
\(N^\alpha_\theta(p)\)-quasi-Cauchy sequence of points
in \(A\), where a sequence \((x_k)\) of points in \(\mathbb{R}\) is called
\(N^\alpha_\theta(p)\)-quasi-Cauchy if
\[\lim_{r\rightarrow\infty}\frac{1}{h^\alpha_r}\Sigma_{k\in I_r}|\Delta x_k|^p=0,\]
where \(\Delta x_k = x_{k+1} - x_k\) for each positive integer \(k, p\) is a constant positive integer, \(\alpha\) is a constant in \(]0; 1],
I_r = (k_{r-1}; k_r]\), and \(\theta = (k_r)\) is a lacunary sequence, that is, an increasing sequence of positive integers such
that \(k_0 \neq 0\), and \(h_r : k_r - k_{r-1} \rightarrow\infty\). Some other function spaces are also investigated.
4371
4380
Huseyin
Kaplan
Department of Mathematics, Faculty of science and letters
Nigde University
Turkey
hkaplan@nigde.edu.tr
Huseyin
Cakalli
Graduate School of Science and Engineering
Maltepe University
Turkey
hcakalli@gmail.com
Summability
strongly lacunary convergence
quasi-Cauchy sequences
boundedness
uniform continuity.
Article.77.pdf
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[1]
D. Burton, J. Coleman, Quasi-Cauchy Sequences , Amer. Math. Monthly, 117 (2010), 328-333
##[2]
H. Cakalli , Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math., 26 (1995), 113-119
##[3]
H. Çakalli, Introduction to General Topology, (First Volume), Istanbul University Faculty of Science Publication, ISBN: 975-404-465-1., Istanbul (1997)
##[4]
H. Cakalli , Slowly oscillating continuity, Abstr. Appl. Anal., 2008 (2008), 1-5
##[5]
H. Cakalli, Sequential definitions of compactness, Appl. Math. Lett., 21 (2008), 594-598
##[6]
H. Cakalli, Forward continuity , J. Comput. Anal. Appl., 13 (2011), 225-230
##[7]
H. Cakalli , On G-continuity , Comput. Math. Appl., 61 (2011), 313-318
##[8]
H. Cakalli, \(\delta\)-quasi-Cauchy sequences, Math. Comput. Modelling, 53 (2011), 397-401
##[9]
H. Cakalli , On \(\Delta\)-quasi-slowly oscillating sequences , Comput. Math. Appl., 62 (2011), 3567-3574
##[10]
H. Cakalli, Statistical quasi-Cauchy sequences, Math. Comput. Modelling, 54 (2011), 1620-1624
##[11]
H. Cakalli , Statistical ward continuity, Appl. Math. Lett., 24 (2011), 1724-1728
##[12]
H. Cakalli, Sequential definitions of connectedness, Appl. Math. Lett., 25 (2012), 461-465
##[13]
H. Cakalli, N-theta-Ward continuity, Abstr. Appl. Anal., 2012 (2012), 1-8
##[14]
H. Cakalli , A variation on ward continuity, Filomat, 27 (2013), 1545-1549
##[15]
H. Cakalli , Variations on quasi-Cauchy sequences, Filomat, 29 (2015), 13-19
##[16]
H. Cakalli, M. Albayrak , New Type Continuities via Abel Convergence, Sci. World J., 2014 (2014), 1-6
##[17]
H. Cakalli, C. G. Aras, A. Sonmez, Lacunary statistical ward continuity, Proceedings of the International Conference on Advancements in Mathematical Sciences, (2015)
##[18]
H. Cakalli, P. Das, Fuzzy compactness via summability, Appl. Math. Lett., 22 (2009), 1665-1669
##[19]
H.Çakalli, B. Hazarika , Ideal Quasi-Cauchy sequences , J. Inequal. Appl., 2012 (2012), 1-11
##[20]
H. Çakalli, H. Kaplan, A study on N-theta quasi-Cauchy sequences, Abstr. Appl. Anal., 2013 (2013), 1-4
##[21]
H. Çakalli, M. K. Khan, Summability in Topological Spaces, Appl. Math. Lett., 24 (2011), 348-352
##[22]
H. Çakalli, R. F. Patterson , Functions preserving slowly oscillating double sequences, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 2013 (2013), -
##[23]
H. Çakalli, A. Sonmez, Slowly oscillating continuity in abstract metric spaces, Filomat, 27 (2013), 925-930
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H. Çakalli, A. Sonmez, C. G. Aras, \(\lambda\)-statistically ward continuity , An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 2015 (2015), 1-12
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H. akalli, A. Sonmez, C. Genç, On an equivalence of topological vector space valued cone metric spaces and metric spaces, Appl. Math. Lett., 25 (2012), 429-433
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I. Canak, M. Dik, New types of continuities, Abstr. Appl. Anal., 2010 (2010), 1-6
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M. Et, H. Şengül, Some Cesaro-Type Summability Spaces of Order alpha and Lacunary Statistical Convergence of Order alpha, Filomat, 28 (2014), 1593-1602
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H. Şengül, M. Et, On lacunary statistical convergence of order alpha, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 473-482
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]
Some fixed point theorems in modular metric spaces
Some fixed point theorems in modular metric spaces
en
en
In this work, we discuss the defnition of the Reich contraction single or multivalued mappings defined
in a modular metric space. In our investigation, we prove the existence of fixed point results for these
mappings.
4381
4387
Afrah A. N.
Abdou
Department of Mathematics
King Abdulaziz University
Saudi Arabia
aabdou@kau.edu.sa
\(\Delta_2\)-condition
fixed point
modular metric spaces
multivalued contraction mapping.
Article.78.pdf
[
[1]
A. A. N. Abdou, M. A. Khamsi , Fixed point results of pointwise contractions in modular metric spaces , Fixed Point Theory Appl., 2013 (2013), 1-11
##[2]
A. A. N. Abdou, M. A. Khamsi , Fixed points of multivalued contraction mappings in modular metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-10
##[3]
S. Banach , Sur les operations dans les ensembles abstraits et leure application aux equations integrals, Fund. Math., 3 (1922), 133-181
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V. V. Chistyakov , Modular metric spaces, I: Basic concepts , Nonlinear Anal., 72 (2010), 1-14
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V. V. Chistyakov , Modular metric spaces, II: Application to superposition operators, Nonlinear Anal., 72 (2010), 15-30
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T. Dominguez Benavides, M. A. Khamsi, S. Samadi , Uniformly Lipschitzian mappings in modular function spaces, Nonlinear Anal., 46 (2001), 267-278
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M. A. Khamsi, W. A. Kirk , An Introduction to Metric Spaces and Fixed Point Theory, John Wiley, New York (2001)
##[8]
M. A. Khamsi, W. M. Kozlowski , Fixed Point Theory in Modular Function Spaces , Birkhäuser/Springer, Cham (2015)
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W. M. Kozlowski , Modular Function Spaces, Dekker, New York, Basel (1988)
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]
Covering properties defined by semi-open sets
Covering properties defined by semi-open sets
en
en
We study certain covering properties in topological spaces by using semi-open covers. A part of this
article deals with Menger-type covering properties. The notions of s-Menger, almost s-Menger, star s-
Menger, almost star s-Menger, strongly star s-Menger spaces are defined and corresponding properties are
investigated.
4388
4398
Amani
Sabah
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
amani.sabah@yahoo.com
Moiz ud Din
Khan
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
moiz@comsats.edu.pk
Ljubiša D. R.
Kočinac
Faculty of Sciences and Mathematics
University of Niš
Serbia
lkocinac@gmail.com
Semi-open set
(star) semi-compact space
semi-Lindelöf space
s-Menger space
star s-Menger space.
Article.79.pdf
[
[1]
O. T. Alas, L. R. Junqueira, R. G. Wilson , Countability and star covering properties, Topology Appl., 158 (2011), 620-626
##[2]
D. R. Anderson, J. A. Jensen, Semi-continuity on topological spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci Fis. Mat. Natur., 42 (1967), 782-783
##[3]
D. Andrijević , Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32
##[4]
S.-S. Chang, Y. J. Cho, S. M. Kang , Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, New York (2001)
##[5]
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Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications
Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications
en
en
In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems
in abstract convex spaces. By virtue of the properties of \(\Gamma\)-convex and KC-map, we give some sufficient
conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium
problems in abstract convex spaces. As application, we show an existence theorem of solutions for the
generalized semi-infinite programs with generalized symmetric vector quasi-equilibrium constraints.
4399
4408
Wei-Bing
Zhang
Department of Information and computing science
Chengdu Technological University
P. R. China
scu_zwb@126.com
Wen-Yong
Yan
Department of Information and computing science
Chengdu Technological University
P. R. China
1051671804@qq.com
Abstract convex space
generalized symmetric vector quasi-equilibrium problem
semi-infinite program
\(\Gamma\)-convex
KKM mapping.
Article.80.pdf
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]
Strong convergence theorems for maximal monotone operators and continuous pseudocontractive mappings
Strong convergence theorems for maximal monotone operators and continuous pseudocontractive mappings
en
en
We introduce a new iterative algorithm for finding a common element of the solution set of the variational
inequality problem for a continuous monotone mapping, the zero point set of a maximal monotone operator,
and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish
strong convergence of the sequence generated by the proposed algorithm to a common point of three sets,
which is a solution of a certain variational inequality. Further, we find the minimum-norm element in
common set of three sets. As applications, we consider iterative algorithms for the equilibrium problem
coupled with fixed point problem.
4409
4426
Jong Soo
Jung
Department of Mathematics
Dong-A University
Korea
jungjs@dau.ac.kr
Maximal monotone operator
continuous monotone mapping
continuous pseudocontractive mapping
fixed points
variational inequality
zeros
minimum-norm point.
Article.81.pdf
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Y. Yao, Y. J. Cho, Y.-C. Liou, Agorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems, European J. Oper. Res., 212 (2011), 242-250
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Y. Yao, Y.-C. Liou, J-C. Yao, Finding the minimum norm common element of maximal monotone operators and nonexpansive mappings without involving projection, J. Nonlinear Convex Anal., 16 (2015), 835-853
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H. Zegeye, An iterative approximation method for a common fixed point of two pseudocontractive mappings, ISRN Math. Anal., 2011 (2011), 1-14
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H. Zegeye, N. Shahzad , Strong convergence of an iterative method for pseudo-contractive and monotone mappings, J. Global Optim., 54 (2012), 173-184
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S. S. Zhang, H. H. W. Lee, C. K. Chan, Algorithms of common solutions to quasi variational inclusion and fixed point problems , Appl. Math. Mechanics, 29 (2008), 571-581
]
Optimal derivative-free root finding methods based on the Hermite interpolation
Optimal derivative-free root finding methods based on the Hermite interpolation
en
en
We develop n-point optimal derivative-free root finding methods of order \(2^n\), based on the Hermite
interpolation, by applying a first-order derivative transformation. Analysis of convergence confirms that
the optimal order of convergence of the transformed methods is preserved, according to the conjecture of
Kung and Traub. To check the effectiveness and reliability of the newly presented methods, different type
of nonlinear functions are taken and compared.
4427
4435
Nusrat
Yasmin
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University Multan
Pakistan
nusyasmin@yahoo.com
Fiza
Zafar
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University Multan
Pakistan
fizazafar@gmail.com
Saima
Akram
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University Multan
Pakistan
saimaakram@bzu.edu.pk
Root finding methods
optimal order of convergence
derivative approximation
Hermite interpolation.
Article.82.pdf
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[1]
A. Cordero, J. R. Torregrosa, Low-complexity root-finding iteration functions with no derivatives of any order of convergence, J. Comput. Appl. Math., 275 (2015), 1-502
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Y. H. Geum, Y. I. Kim , A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function, J. Comput. Appl. Math., 235 (2011), 3178-3188
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H. T. Kung, J. F. Traub, Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Mach., 21 (1974), 643-651
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M. S. Petković, B. Neta, L. D. Petković, J. Džunić, Multipoint methods for solving nonlinear equations, Elsevier, Amsterdam (2013)
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M. S. Petković, L. D. Petković , Families of optimal multipoint methods for solving nonlinear equations: A Survey , Appl. Anal. Discrete Math., 4 (2010), 1-22
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S. Sharifi, M. Salimi, S. Siegmund, T. Lotfi, A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations, Math. Comput. Simulation, 119 (2016), 69-90
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F. Soleymani, S. Shateyi, H. Salmani, Computing simple roots by an optimal sixteenth-order class, J. Appl. Math., 2012 (2012), 1-13
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I. F. Steffensen, Remarks on iteration , Candinavian Actuarial J., 16 (1933), 64-72
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F. Zafar, N. Hussain, Z. Fatima, A. Kharal, Optimal sixteenth order convergent method based on Quasi-Hermite interpolation for computing roots, Sci. World J., 2014 (2014), 1-18
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F. Zafar, N. Yasmin, S. Akram, M. D. Junjua, A general class of derivative free optimal root finding methods based on rational interpolation, Sci. World J., 2015 (2015), 1-12
]
Fixed point theorems for improved \(\alpha\)-Geraghty contractions in partial metric spaces
Fixed point theorems for improved \(\alpha\)-Geraghty contractions in partial metric spaces
en
en
Rosa and Vetro [V. La Rosa, P. Vetro, J. Nonlinear Sci. Appl., 7 (2014), 1-10] established new fixed
point results in complete partial metric spaces.
In this paper, we improve the notion of \(\alpha\)-Geraghty contraction type mappings and establish some
common fixed point theorems for a pair of \(\alpha\)-admissible mappings under an improved notion of \(\alpha\)-Geraghty
contraction type mappings in complete partial metric spaces. We give an example to illustrate these results.
An application of main result to the existence of solution of system of integral equations is also presented.
4436
4449
Muhammad
Nazam
Department of Mathematics and Statistics
International Islamic University
Pakistan
nazim.phdma47@iiu.edu.pk
Muhammad
Arshad
Department of Mathematics and Statistics
International Islamic University
Pakistan
marshadzia@iiu.edu.pk
Choonkil
Park
Research Institute for Natural Sciences
Hanyang University
Republic of Korea
baak@hanyang.ac.kr
Fixed point
\(\alpha\)-Geraghty contraction
partial metric space.
Article.83.pdf
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[1]
M. Abbas, T. Nazir, S. Romaguera, Fixed point results for generalized cyclic contraction mappings in partial metric spaces, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 106 (2012), 287-297
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T. Abdeljawad , Meir-Keeler \(\alpha\)-contractive fixed and common fixed point theorems, Fixed Point Theory Appl., 2013 (2013), 1-10
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T. Abdeljawad, E. Karapnar, K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
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M. U. Ali, T. Kamran, On (\(\alpha-\psi\) )-contractive multi-valued mappings, Fixed Point Theory Appl., 2013 (2013), 1-7
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S. Chandok, Some fixed point theorems for (\(\alpha,\beta\))-admissible Geraghty type contractive mappings and related results, Math. Sci., 9 (2015), 127-135
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S.-H. Cho, J.-S. Bae, E. Karapinar , Fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-11
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I. M. Erhan, E. Karapinar, D. Türkoğlu , Different types Meir-Keeler contractions on partial metric spaces , J. Comput. Anal. Appl., 14 (2012), 1000-1005
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M. A. Geraghty , On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), 604-608
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N. Hussain, E. Karapinar, P. Salimi, F. Akbar, \(\alpha\)-admissible mappings and related fixed point theorems , J. Inequal. Appl., 2013 (2013), 1-11
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V. La Rosa, P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces , J. Nonlinear Sci. Appl., 7 (2014), 1-10
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J. Martinez-Moreno, W. Sintunavarat, Y. J. Cho , Common fixed point theorems for Geraghty's type contraction mappings using the monotone property with two metrics, Fixed Point Theory Appl., 2015 (2015), 1-15
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C. Mongkolkehai, Y. J. Cho, P. Kumam, Best proximity points for Geraghty's proximal contraction mappings, Fixed Point Theory Appl., 2013 (2013), 1-17
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P. Salimi, A. Latif, N. Hussain, Modied \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 1-19
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
]
A rough Marcinkiewicz integral along smooth curves
A rough Marcinkiewicz integral along smooth curves
en
en
We consider the boundedness of a kind of nonlinear integral operators on \(L^p\) spaces. Including the
parametric Marcinkiewicz integrals with rough kernels along compound curves \(\{\Phi(\varphi(|y|))y'; y\in \mathbb{R}^n\}\) with
\(\Phi\) satisfying certain growth conditions and \(\varphi\) being differentiable function with monotonicity and some
properties on the positive real line, we investigate the \(L^p\) bounds of these operators under the integral
kernels given by the sphere functions \(\Omega\)
in \(H^1(S^{n-1})\) or \(\Omega\)
in \(L(\log^+ L)^{\frac{1}{2}}(S^{n-1})\) and the radial function
\(h \in \Delta_\gamma(\mathbb{R}^+)\). As applications, the corresponding results for parametric Marcinkiewicz integral operators
related to area integrals and Littlewood-Paley \(g^*_\lambda\)
-functions are presented.
4450
4464
Feng
Liu
College of Mathematics and Systems Science
Shandong University of Science and Technology
China
liufeng860314@163.com
Zunwei
Fu
Department of Mathematics
The University of Suwon
Korea
zwfu@mail.bnu.edu.cn
Yanpeng
Zheng
Department of Information and Telecommunications Engineering
The University of Suwon
Korea
zhengyanpeng0702@sina.com
Qing
Yuan
Department of Mathematics
Linyi University
China
zjyuanq@yeah.net
Parametric Marcinkiewicz
rough kernels
Hardy spaces
Fourier transform estimates.
Article.84.pdf
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[1]
H. M. Al-Qassem, A. Al-Salman, A note on Marcinkiewicz integral operators, J. Math. Anal. Appl., 282 (2003), 698-710
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A. Al-Salman, Y. Pan, Singular integrals with rough kernels in \(L \log^+ L(S^{n-1})\) , J. London Math. Soc., 66 (2002), 153-174
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L. Colzani, Hardy spaces on spheres, PhD thesis, Washington University, St. Louis (1982)
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]
Global attractivity of a rational difference equation of order ten
Global attractivity of a rational difference equation of order ten
en
en
In this paper, we study qualitative properties and periodic nature of the solutions of the difference
equation
\[x_{n+1} = ax_{n-4} +\frac{ bx^2_{ n-4}}{ cx_{n-4} + dx_{n-9}} ; \qquad n = 0; 1; ...;\]
where the initial conditions \(x_{-9}; x_{-8}; x_{-7}; x_{-6}; x_{-5}; x_{-4}; x_{-3}; x_{-2}; x_{-1}; x_0\) are arbitrary positive real
numbers and \(a; b; c; d\) are constants. Also we obtain the form of solutions of some special cases of this
equation.
4465
4477
Abdul
Khaliq
Riphah Institute of Computing Applied Sciences (RICAS), Department of Mathematics
Riphah International University, Lahore Campus.
khaliqsyed@gmail.com
Faris
Alzahrani
Mathematics Department, Faculty of Science
King Abdulaziz University
Saudi Arabia
faris.kau@hotmail.com
E. M.
Elsayed
Mathematics Department, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Mansoura University
Saudi Arabia
Egypt
emmelsayed@yahoo.com
Periodicity
stability
rational difference equations.
Article.85.pdf
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##[2]
Q. Din, Qualitative nature of a discrete predator-prey system , Contemp. Methods Math. Phys. Gravit., 1 (2015), 27-42
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Q. Din, E. M. Elsayed, Stability analysis of a discrete ecological model , Comput. Ecol. Soft., 4 (2014), 89-103
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M. M. El-Dessoky, E. M. Elsayed, On the solutions and periodic nature of some systems of rational difference equations, J. Comput. Anal. Appl., 18 (2015), 206-218
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H. El-Metwally, E. M. Elsayed, Solution and behavior of a third rational difference equation, Util. Math., 88 (2012), 27-42
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H. El-Metwally, E. M. Elsayed , Qualitative behavior of some rational difference equations, J. Comput. Anal. Appl., 20 (2016), 226-236
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E. M. Elsayed , Solution and attractivity for a rational recursive sequence, Discrete Dyn. Nat. Soc., 2011 (2011), 1-17
##[10]
E. M. Elsayed , Solutions of rational difference system of order two, Math. Comput. Modelling, 55 (2012), 378-384
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E. M. Elsayed , Behavior and expression of the solutions of some rational difference equations, J. Comput. Anal. Appl., 15 (2013), 73-81
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E. M. Elsayed, Solution for systems of difference equations of rational form of order two, Comput. Appl. Math., 33 (2014), 751-765
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E. M. Elsayed, On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath., 7 (2014), 1-26
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E. M. Elsayed, A. M. Ahmed, Dynamics of a three-dimensional systems of rational difference equations , Math. Methods Appl. Sci., 39 (2016), 1026-1038
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E. M. Elsayed, H. El-Metwally , Global behavior and periodicity of some difference equations, J. Comput. Anal. Appl., 19 (2015), 298-309
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E. M. Elsayed, M. M. El-Dessoky , Dynamics and global behavior for a fourth-order rational difference equation, Hacet. J. Math. Stat., 42 (2013), 479-494
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E. M. Elsayed, M. M. El-Dessoky, E. O. Alzahrani , The form of the solution and dynamics of a rational recursive sequence, J. Comput. Anal. Appl., 17 (2014), 172-186
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E. M. Elsayed, M. M. El-Dessoky, Asim Asiri , Dynamics and behavior of a second order rational difference equation, J. Comput. Anal. Appl., 16 (2014), 794-807
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E. M. Elsayed, T. F. Ibrahim, Solutions and periodicity of a rational recursive sequences of order five, Bull. Malays. Math. Sci. Soc., 38 (2015), 95-112
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E. M. Elsayed, T. F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations, Hacet. J. Math. Stat., 44 (2015), 1361-1390
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E. M. Elsayed, M. Mansour, M. M. El-Dessoky, Solutions of fractional systems of difference equations, Ars Combin., 110 (2013), 469-479
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A. Gelisken, M. Kara, Some general systems of rational difference equations, J. Differ. Equ., 2015 (2015), 1-7
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E. A. Grove, G. Ladas, L. C. McGrath, C. T. Teixeira, Existence and behavior of solutions of a rational system , Comm. Appl. Nonlinear Anal., 8 (2001), 1-25
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Y. Halim , Global character of systems of rational difference equations, Electron. J. Math. Anal. Appl., 3 (2015), 204-214
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T. F. Ibrahim, N. Touafek, Max-type system of difference equations with positive two-periodic sequences, Math. Methods Appl. Sci., 37 (2014), 2541-2553
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D. Jana, E. M. Elsayed, Interplay between strong Allee effect, harvesting and hydra effect of a single population discrete-time system, Int. J. Biomath., 9 (2016), 1-25
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R. Karatas, C. Cinar, D. Simsek, On positive solutions of the difference equation \(x_{n+1} = \frac{x_{n-5} }{1 + x_{n-2}x_{n-5}} \); , Int. J. Contemp. Math. Sci., 1 (2006), 495-500
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A. Khaliq, E. M. Elsayed , Qualitative properties of difference equation of order six, Math., 4 (2016), 1-24
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A. Q. Khan, M. N. Qureshi , Global dynamics of a competitive system of rational difference equations, Math. Methods Appl. Sci., 38 (2015), 4786-4796
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H. Ma, H. Feng , On Positive Solutions for the Rational Difference Equation Systems \(x_{n+1} = \frac{A x_n}{y^2_n}\) and \( y_{n+1} = \frac{By_n }{x_{n-1}y_{n-1}}\), Int. Scho. Res. Not., 2014 (2014), 1-4
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S. Sarif Hassan, E. Chatterjee, Dynamics of the equation \(z_{n+1} =\frac{ \alpha+\beta z_n}{ A+z_{n-1}}\) in the complex plane, Cogent Math., 2 (2015), 1-12
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D. Tollu, Y. Yazlik, N. Taskara , The Solutions of Four Riccati Difference Equations Associated with Fibonacci Numbers, Balkan J. Math., 2 (2014), 163-172
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N. Touafek, E. M. Elsayed, On the solutions of systems of rational difference equations, Math. Comput. Modelling, 55 (2012), 1987-1997
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I. Yalçınkaya, On the dynamics of the difference equation \(x_{n+1} = \frac{ax_{n-k}}{ b + cx^p_ n}\), Fasc. Math., 42 (2009), 133-139
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I. Yalçınkaya, C. Cinar, On the difference equation \(x_{n+1} = \alpha +\frac{ x_{n-m} }{x^k_ n}\), Discrete Dyn. Nat. Soc., 2008 (2008), 1-8
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Y. Yazlik, E. M. Elsayed, N. Taskara, On the behaviour of the solutions of difference equation systems, J. Comput. Anal. Appl., 16 (2014), 932-941
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E. M. E. Zayed, Qualitative behavior of a rational recursive sequence \(x_{n+1} = Ax_n + Bx_{n-k} +\frac{ p + x_{n-k} }{qx_n + x{n-k}} \), International Journal of Advances in Mathematics, 1 (2014), 44-55
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Q. Zhang, W. Zhang, J. Liu, Y. Shao, On a fuzzy logistic difference equation, WSEAS Trans. Math., 13 (2014), 282-290
]
Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces
Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces
en
en
The purpose of this paper is to introduce the implicit midpoint rule of asymptotically nonexpansive
mappings in Hilbert spaces. The strong convergence of this viscosity method is proved under certain assumptions
imposed on the sequence of parameters. Moreover, it is shown that the limit solves an additional
variational inequality. Applications to nonlinear variational inclusion problem, nonlinear Volterra integral
equations, variational inequality problem and hierarchical minimization problems are included. The results
presented in the paper extend and improve some recent results announced in the current literature.
4478
4488
Liang-Cai
Zhao
College of Mathematics
Yibin University
P. R. China
Shih-Sen
Chang
Center for General Education
China Medical University
Taiwan
changss2013@163.com
Ching-Feng
Wen
Center for Fundamental Science
Kaohsiung Medical University
Taiwan
Viscosity
implicit midpoint rule
asymptotically nonexpansive mapping
projection
variational inequality.
Article.86.pdf
[
[1]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H. K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), 1-9
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H. Attouch, Viscosity solutions of minimization problems, SIAM J. Optim., 6 (1996), 769-806
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W. Auzinger, R. Frank , Asymptotic error expansions for stiff equations: an analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case, Numer. Math., 56 (1989), 469-499
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G. Bader, P. Deu hard , A semi-implicit mid-point rule for stiff systems of ordinary differential equations, Numer. Math., 41 (1983), 373-398
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S. Somali, Implicit midpoint rule to the nonlinear degenerate boundary value problems, Int. J. Comput. Math., 79 (2002), 327-332
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P. Sunthrayuth, Y. J. Cho, P. Kumam , Viscosity approximation methods for zeros of accretive operators and fixed point problems in Banach spaces, Bull. Malays. Math. Sci. Soc., 39 (2016), 773-793
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H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
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H. K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-12
]
Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems in \(M\)-metric spaces
Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems in \(M\)-metric spaces
en
en
In this paper, we introduce several types of Ulam-Hyers stability, well-posedness and limit shadowing
property of the fixed point problem in \(M\)-metric spaces. Also, we give such results for fixed point problems
of Banach and Kannan contractive mappings in \(M\)-metric spaces and provide two examples to illustrate the
results presented herein.
4489
4499
Adoon
Pansuwan
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
pansuwan@mathstat.sci.tu.ac.th
Wutiphol
Sintunavarat
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
wutiphol@mathstat.sci.tu.ac.th
Jae Young
Choi
Department of Mathematics Education
Gyeongsang National University
Korea
darksoul83@naver.com
Yeol Je
Cho
Department of Mathematics Education
Center for General Education
Gyeongsang National University
China Medical University
Korea
Taiwan
yjcho@gnu.ac.kr
Fixed point
limit shadowing property
M-metric space
Ulam-Hyers stability
well-posedness.
Article.87.pdf
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[1]
K. Abodayeh, N. Mlaiki, T. Abedljawad, W. Shatanawi , Relations between partial metrics and M-metrics, Caristi- Kirk's theorem in M-metric type spaces, J. Math. Anal., ( to appear), -
##[2]
M. Asadi, Fixed point theorems for Meir-Keeler type mappings in M-metric spaces with applications, Fixed Point Theory Appl., 2015 (2015), 1-10
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M. Asadi, E. Karapinar, P. Salimi , New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014 (2014), 1-9
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A. Azam, F. Brian, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32 (2011), 243-253
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M. F. Bota, E. Karapinar, O. Mlesnite, Ulam-Hyers stability results for fixed point problems via \(\alpha-\psi\) -contractive mapping in (b)-metric space, Abstr. Appl. Anal., 2013 (2013), 1-6
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M. F. Bota-Boriceanu, A. Petrusel, Ulam-Hyers stability for operatorial equations, An. Stiint. Univ. Al. I. Cuza Iasi. Mat., 57 (2011), 65-74
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]
Almost periodic solutions for a nonlinear integro-differential equation with neutral delay
Almost periodic solutions for a nonlinear integro-differential equation with neutral delay
en
en
This paper is concerned with the existence of almost periodic and pseudo almost solutions for a nonlinear
integro-differential equation with neutral delay, which arise in epidemic problems. By using almost periodic
functions theory and fixed point theory, we obtain the results. Two examples are given to illustrate our
results. In addition, an application to nonautonomous differential equations is also given.
4500
4508
Qiu-Feng
Zou
College of Mathematics and Information Science
Jiangxi Normal University
P. R. China
642074260@qq.com
Hui-Sheng
Ding
College of Mathematics and Information Science
Jiangxi Normal University
P. R. China
dinghs@mail.ustc.edu.cn
Almost periodic
pseudo almost periodic
integro-differential
neutral delay.
Article.88.pdf
[
[1]
E. Ait Dads, P. Cieutat, L. Lhachimi, Positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations, Math. Comput. Modelling, 49 (2009), 721-739
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E. Ait Dads, P. Cieutat, L. Lhachimi , Existence of positive almost periodic or ergodic solutions for some neutral integral equations, Differ. Integral Equ., 22 (2009), 1075-1096
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E. Ait Dads, K. Ezzinbi , Existence of positive pseudo almost periodic solution for a class of functional equations arising in epidemic problems, Cybern. Syst. Anal., 30 (1994), 133-144
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E. Ait Dads, K. Ezzinbi, Almost periodic solution for some neutral nonlinear integral equation , Nonlinear Anal., 28 (1997), 1479-1489
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A. Bellour, E. Ait Dads, Periodic solutions for nonlinear neutral delay integro-differential equations, Electron. J. Differential Equations, 100 (2015), 1-9
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T. Diagana, Almost automorphic type and almost periodic type functions in abstract spaces, Springer, New York (2013)
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H.-S. Ding, Y.-Y. Chen, G. M. N'Guérékata, Existence of positive pseudo almost periodic solutions to a class of neutral integral equations, Nonlinear Anal., 74 (2011), 7356-7364
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H.-S. Ding, Y.-Y. Chen, G. M. N'Guerekata , \(C^n\)-almost periodic and almost periodic solutions for some nonlinear integral equations, Electron. J. Qual. Theory Differ. Equ., 6 (2012), 1-13
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H. S.-Ding, G. M. N'Guérékata , A note on the existence of positive bounded solutions for an epidemic model, Appl. Math. Lett., 26 (2013), 881-885
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Global and local R-linear convergence of a spectral projected gradient method for convex optimization with singular solution
Global and local R-linear convergence of a spectral projected gradient method for convex optimization with singular solution
en
en
In this paper, we propose a spectral projected gradient method for the convex optimization problem
with singular solution. By solving the equivalent equation of the gradient function, this method combines
the perturbed spectral gradient direction with the projection direction to generate the next iteration point.
Under some mild conditions, we establish the global convergence and the local R-linear convergence rate
under the local error bound condition. Preliminary numerical tests are given to show that the proposed
method works well.
4509
4519
Zhensheng
Yu
College of Science
University of Shanghai for Science and Technology
P. R. China
zhsh-yu@163.com
Xinyue
Gan
College of Science
University of Shanghai for Science and Technology
P. R. China
Unconstrained optimization
spectral projected gradient
local error bound
R-linear convergence.
Article.89.pdf
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]
The corresponding inverse of functions of multidual complex variables in Clifford analysis
The corresponding inverse of functions of multidual complex variables in Clifford analysis
en
en
We aim to investigate the differentiability of multidual functions and the notion of the hyperholomorphicity to multidual-valued functions. Also, we provide the basic statements which extend holomorphic
functions to the higher multidual generalized Clifford analysis.
4520
4528
Ji Eun
Kim
Department of Mathematics
Pusan National University
Republic of Korea
jeunkim@pusan.ac.kr
Differentiability
multidual functions
hyperholomorphicity
Clifford analysis.
Article.90.pdf
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[1]
P. Agarwal, J. Choi, R. B. Paris, Extended Riemann-Liouville fractional derivative operator and its applications, J. Nonlinear Sci. Appl., 8 (2015), 451-466
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J. E. Kim, S. J. Lim, K. H. Shon, Regular functions with values in ternary number system on the complex Clifford analysis, Abstr. Appl. Anal., 2013 (2013), 1-7
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J. E. Kim, S. J. Lim, K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal., 2014 (2014), 1-8
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J. E. Kim, K. H. Shon, The Regularity of functions on Dual split quaternions in Clifford analysis, Abstr. Appl. Anal., 2014 (2014), 1-8
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J. E. Kim, K. H. Shon, Polar coordinate expression of hyperholomorphic functions on split quaternions in Clifford analysis, Adv. Appl. Clifford Algebr., 25 (2015), 915-924
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J. E. Kim, K. H. Shon, Coset of a hypercomplex number system in Clifford analysis, Bull. Korean Math. Soc., 52 (2015), 1721-1728
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J. E. Kim, K. H. Shon, Inverse mapping theory on split quaternions in Clifford analysis, Filomat, 30 (2016), 1883-1890
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J. E. Kim, K. H. Shon, Properties of regular functions with values in bicomplex numbers, Bull. Korean Math. Soc., 53 (2016), 507-518
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A. P. Kotelnikov, Screw calculus and some applications to geometry and mechanics, Annals of Imperial University of Kazan, (1895)
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D. Kumar, S. D. Purohit, J. Choi, Generalized fractional integrals involving product of multivariable H-function and a general class of polynomials, J. Nonlinear Sci. Appl., 9 (2016), 8-21
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X. Wang, D. Han, C. Yu, Z. Zheng, The geometric structure of unit dual quaternion with application in kinematic control, J. Math. Anal. Appl., 389 (2012), 1352-1364
]
Exact solutions and dynamics of generalized AKNS equations associated with the nonisospectral depending on exponential function
Exact solutions and dynamics of generalized AKNS equations associated with the nonisospectral depending on exponential function
en
en
No matter constructing or solving nonlinear evolution equations (NLEEs), it is important and interesting
in the field of nonlinear science. In this paper, generalized Ablowitz-Kaup-Newell{Segur (AKNS) equations
are constructed and solved exactly. To be specific, the famous AKNS spectral problem is first generalized by
embedding a nonisospectral parameter whose varying with time obeys the exponential function of spectral
parameter. Based on the generalized AKNS spectral problem and its corresponding time evolution equation,
we then derive a generalized AKNS equation with infinite number of terms. Furthermore, exact solutions of
the generalized AKNS equations are formulated through the inverse scattering transform method. Finally, in
the case of reflectionless potentials, the obtained exact solutions are reduced to explicit n-soliton solutions.
It is shown that the dynamical evolutions of such soliton solutions possess not only time-varying speeds and
amplitudes but also singular points in the process of propagations.
4529
4541
Sheng
Zhang
School of Mathematics and Physics
Bohai University
China
szhangchina@126.com
Xudong
Gao
School of Mathematics and Statistics
Kashgar University
China
986242791@qq.com
Exact solution
n-soliton solution
dynamical evolution
generalized AKNS equations
inverse scattering transform.
Article.91.pdf
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]
On the construction of three step derivative free four-parametric methods with accelerated order of convergence
On the construction of three step derivative free four-parametric methods with accelerated order of convergence
en
en
In this paper, a general procedure to develop some four-parametric with-memory methods to find simple
roots of nonlinear equations is proposed. The new methods are improved extensions of with derivative with-
out memory iterative methods. We used four self-accelerating parameters to boost up the convergence order
and computational efficiency of the proposed methods without using any additional function evaluations.
Numerical examples are presented to support the theoretical results of the methods. We further investigate
the dynamics of the methods in the complex plane.
4542
4553
Fiza
Zafar
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Pakistan
fizazafar@gmail.com
Saima
Akram
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Pakistan
saimaakram@bzu.edu.pk
Nusrat
Yasmin
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Pakistan
nusyasmin@yahoo.com
Moin-ud-Din
Junjua
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Pakistan
moin_junjua@yahoo.com
Root finding
four-parametric
accelerated order of convergence
derivative free.
Article.92.pdf
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C. Chun , Some variants of King's fourth-order family of methods for nonlinear equations, Appl. Math. Comput., 190 (2007), 57-62
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A. Cordero, T. Lotfi, P. Bakhtiari, J. R. Torregrosa, An efficient two-parametric family with-memory for nonlinear equations, Numer. Algorithms, 68 (2015), 323-335
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A. Cordero, J. R. Torregrosa, Low-complexity root-finding iteration functions with no derivatives of any order of convergence , J. Comput. Appl. Math., 275 (2015), 502-515
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J. Džunić, M. S. Petković , On generalized multipoint root-solvers with memory, J. Comput. Appl. Math., 236 (2012), 2909-2920
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Q. Zheng, J. Li, F. Huang, An optimal Steffensen-type family for solving nonlinear equations, Appl. Math. Comput., 217 (2011), 9592-9597
]
Stability of Pexiderized quadratic functional equation on a set of measure zero
Stability of Pexiderized quadratic functional equation on a set of measure zero
en
en
Let \(\mathbb{R}\) be the set of real numbers and \(Y\) a Banach space. We prove the Hyers-Ulam stability theorem
when \(f; h : \mathbb{R}\rightarrow Y\) satisfy the following Pexider quadratic inequality
\[\|f(x + y) + f(x - y) - 2f(x) - 2h(y)\| \leq\epsilon ;\]
in a set
\(\Omega\subset \mathbb{R}^2\) of Lebesgue measure \(m(\Omega) = 0\).
4554
4562
Iz-iddine
EL-Fassi
Department of Mathematics, Faculty of Sciences
University of Ibn Tofail
Morocco
lzidd-math@hotmail.fr
Abdellatif
Chahbi
Department of Mathematics, Faculty of Sciences
University of Ibn Tofail
Morocco
ab_1980@live.fr
Samir
Kabbaj
Department of Mathematics, Faculty of Sciences
University of Ibn Tofail
Morocco
samkabbaj@yahoo.fr
Choonkil
Park
Research Institute for Natural Sciences
Hanyang University
Korea
aak@hanyang.ac.kr
Pexider quadratic functional equation
Hyers-Ulam stability
first category Lebesgue measure
Baire category theorem.
Article.93.pdf
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]
An affirmative answer to the open questions on the viscosity approximation methods for nonexpansive mappings in CAT(0) spaces
An affirmative answer to the open questions on the viscosity approximation methods for nonexpansive mappings in CAT(0) spaces
en
en
We prove a strong convergence theorem of a two-step viscosity iteration method for nonexpansive mappings
in CAT(0) spaces without the nice projection property \(\mathbb{N}\) and the restriction of the contraction constant
\(k \in [0; \frac{1}{2} )\). Our result gives an affrrmative answer to the open questions raised by Piatek [B. Piatek, Numer.
Funct. Anal. Optim., 34 (2013), 1245-1264], and Kaewkhao et al. [A. Kaewkhao, B. Panyanak, S. Suantai,
J. Inequal. Appl., 2015 (2015), 9 pages].
4563
4570
Shih-Sen
Chang
Center for General Education
China Medical University
Taiwan
changss2013@163.com
Lin
Wang
College of Statistics and Mathematics
Yunnan University of Finance and Economics
P. R. China
WL64mail@aliyun.com;Wanglin64@outlook.com
Gang
Wang
College of Statistics and Mathematics
Yunnan University of Finance and Economics
P. R. China
wg631208@sina.com
Lijuan
Qin
Department of Mathematics
Kunming University
P. R. China
annyqlj@163.com
Viscosity approximation method
fixed point
strong convergence
multivalued nonexpansive mapping
the nice projection property \(\mathbb{N}\)
CAT(0) space.
Article.94.pdf
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Fixed point theorems in ordered cone metric spaces
Fixed point theorems in ordered cone metric spaces
en
en
In this paper, we prove a new fixed point theorem of a nondecreasing and continuous mapping satisfying
some type contractive condition in a partially ordered cone metric space by using \(c\)-distance. Also, we give
a fixed point theorem without the assumption of continuity in a partially ordered cone metric space with
normal cone.
4571
4579
Young-Oh
Yang
Department of Mathematics
Jeju National University
Korea
yangyo@jejunu.ac.kr
Hong Joon
Choi
Department of Mathematics
Jeju National University
Korea
next-xy@hanmail.net
Cone metric space
normal cone
c-distance
common fixed point.
Article.95.pdf
[
[1]
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]
Iterative computation of fixed points of quasi-asymptotic pseudo-contractions
Iterative computation of fixed points of quasi-asymptotic pseudo-contractions
en
en
An iterative algorithm is presented to find the fixed points of a quasi-asymptotic pseudo-contraction in
Hilbert spaces. It is shown that the proposed algorithm converges strongly to the fixed point of a quasiasymptotic
pseudo-contraction.
4580
4588
Yonghong
Yao
Department of Mathematics
Tianjin Polytechnic University
P. R. China
aoyonghong@aliyun.com
Xiaoxue
Zheng
Department of Mathematics
Tianjin Polytechnic University
P. R. China
zhengxiaoxue1991@aliyun.com
Limin
Leng
Department of Mathematics
Tianjin Polytechnic University
P. R. China
lenglimin@aliyun.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics
Kaohsiung Medical University, Kaohsiung 80708
Taiwan
simplex_liou@hotmail.com
Quasi-asymptotic pseudo-contraction
fixed point
iterative algorithm
Hilbert spaces.
Article.96.pdf
[
[1]
L. C. Ceng, H. K. Xu, J. C. Yao, The viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal., 69 (2008), 1402-1412
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Y. Yao, R. P. Agarwal, M. Postolache, Y. C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., 2014 (2014), 1-14
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Y. Yao, Y. C. Liou, J. C. Yao , Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction, Fixed Point Theory Appl., 2015 (2015), 1-19
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Y. Yao, G. Marino, H. K. Xu, Y. C. Liou, Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces, J. Inequal. Appl., 2014 (2014), 1-14
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Y. Yao, M. Postolache, S. M. Kang, Strong convergence of approximated iterations for asymptotically pseudocontractive mappings, Fixed Point Theory Appl., 2014 (2014), 1-13
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H. Zhou, Y. Su , Strong convergence theorems for a family of quasi-asymptotic pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 4047-4052
]
Dynamical behavior for fractional-order shunting inhibitory cellular neural networks
Dynamical behavior for fractional-order shunting inhibitory cellular neural networks
en
en
This paper deals with a class of fractional-order shunting inhibitory cellular neural networks. Applying
the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, some
very verifiable criteria on the existence and uniqueness of nontrivial solution are obtained. Moreover, we
also investigate the uniform stability of the fractional-order shunting inhibitory cellular neural networks.
Finally, an example is given to illustrate our main theoretical findings. Our results are new and complement
previously known results.
4589
4599
Yang
Zhao
Department of Mechanical and Electrical Engineering
Guangdong University of Science and Technology
P. R. China
zhaoyang19781023@gmail.com
Yanguang
Cai
School of Automation
Guangdong University of Technology
P. R. China
caiyg99@163.com
Guobing
Fan
Department of Basic Subjects
Hunan University of Finance and Economics
P. R. China
fgb1953@126.com
Shunting inhibitory cellular neural networks
fractional order
uniform stability.
Article.97.pdf
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X. Huang, Z. Zhao, Z. Wang, Y. X. Li , Chaos and hyperchaos in fractional-order cellular neural networks, Neurocomputing, 94 (2012), 13-21
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F. L. Ren, F. Cao, J. D. Cao, Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks, Neurocomputing, 160 (2015), 185-190
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J. Y. Shao, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays, Phys. Lett. A, 372 (2008), 5011-5016
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F. Wang, Y. Q. Yang, M. F. Hu, Asymptotic stability of delayed fractional-order neural networks with impulsive effects, Neurocomputing, 154 (2015), 239-244
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H. Wang, Y. G. Yu, G. G. Wen, S. Zhang, J. Z. Yu, Global stability analysis of fractional-order Hopfield neural networks with time delay, Neurocomputing, 154 (2015), 15-23
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S. Zhang , Positive solutions for boundary value problems of nonlinear fractional differential equations, Electron. J. Diff. Eqns., 2006 (2006), 1-12
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S. Zhang, Y. G. Yu, H. Wang, Mittag-Leffler stability of fractional-order Hopfield neural networks, Nonlinear Anal. Hybrid Syst., 16 (2015), 104-121
]
On Reich fixed point theorem of \(G\)-contraction mappings on modular function spaces
On Reich fixed point theorem of \(G\)-contraction mappings on modular function spaces
en
en
We define the multivalued Reich (\(G; \rho\))-contraction mappings on a modular function space. Then we
obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we
introduce a \(\rho\)-valued Bernstein operator on the set of functions \(f : [0; 1] \rightarrow L_\rho\) and then give the modular
analogue to Kelisky-Rivlin theorem.
4600
4606
Monther Rashed
Alfuraidan
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Saudi Arabia
monther@kfupm.edu.sa
Bernstein polynomial
directed graph
Reich fixed point theorem
monotone mapping
multivalued mapping
modular function spaces.
Article.98.pdf
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[1]
M. Abbas, S. Ali, P. Kumam, Common Fixed Points in Partially Ordered Modular Function Spaces, J. Ineq. Appl., 2014 (2014), 1-12
##[2]
M. R. Alfuraidan, Remarks on monotone multivalued mappings on a metric space with a graph, J. Ineq. Appl., 2015 (2015), 1-7
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I. Beg, A. R. Butt, Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699-3704
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T. Dominguez Benavides, M. A. Khamsi, S. Samadi, Uniformly Lipschitzian mappings in modular function spaces, Nonlinear Anal., 46 (2001), 267-278
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M. Edelstein, An extension of Banachs contraction principle, Proc. Amer. Math. Soc., 12 (1961), 7-10
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Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl., 317 (2006), 103-112
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J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359-1373
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M. A. Khamsi, W. M. Kozlowski, Fixed point theory in modular function spaces, Birkhäuser-Springer, Cham (2015)
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D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139
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C. Mongkolkeha, P. Kumam, Fixed point theorems for generalized asymptotic pointwise \(\rho\)-contraction mappings involving orbits in Modular function spaces, Appl. Math. Lett., 25 (2012), 1285-1290
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S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2003), 1435-1443
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S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital., 5 (1972), 26-42
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I. A. Rus, Iterates of Bernstein operators, via contraction principle, J. Math. Anal. Appl., 292 (2004), 259-261
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A. Sultana, V. Vetrivel, Fixed points of Mizoguchi-Takahashi contraction on a metric space with a graph and applications, J. Math. Anal. Appl., 417 (2014), 336-344
]
On a degenerate \(\lambda-q\)-Daehee polynomials
On a degenerate \(\lambda-q\)-Daehee polynomials
en
en
Daehee numbers and polynomials are introduced by Kim [T. Kim, Integral Transforms Spec. Funct.,
13 (2002), 65-69] and [D. S. Kim, T. Kim, Appl. Math. Sci. (Ruse), 7 (2013), 5969-5976], and those
polynomials and numbers are generalized by many researchers. In this paper, we make an attempt to
degenerate \(\lambda-q\)-Daehee polynomials, and derive some new and interesting identities and properties of those
polynomials and numbers.
4607
4616
Byung Moon
Kim
Department of Mechanical System Engineering
Dongguk University
Republic of Korea
kbm713@dongguk.ac.kr
Sang Jo
Yun
Department of Mathematics Education
Daegu University, Gyeongsan-si
Republic of Korea
pitt0202@hanmail.net
Jin-Woo
Park
Department of Mathematics Education
Daegu University
Republic of Korea
a0417001@knu.ac.kr
\(\lambda\)-Daehee polynomials
\(q\)-Daehee polynomials
degenerate \(\lambda-q\)-Daehee polynomials.
Article.99.pdf
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[1]
L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51-88
##[2]
Y. K. Cho, T. Kim, T. Mansour, S. H. Rim, Higher-order q-Daehee polynomials, J. Comput. Anal. Appl., 19 (2015), 167-173
##[3]
L. Comtet, Advanced Combinatorics, Reidel Publishing Co., Dordrecht (1974)
##[4]
B. S . El-Desouky, A. Mustafa, New results on higher-order Daehee and Bernoulli numbers and polynomials, Adv. Difference Equ., 2016 (2016), 1-21
##[5]
T. Kim, On q-analogye of the p-adic log gamma functions and related integral, J. Number Theory, 76 (1999), 320-329
##[6]
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys., 9 (2002), 288-299
##[7]
T. Kim, An invariant p-adic integral associated with Daehee numbers, Integral Transforms Spec. Funct., 13 (2002), 65-69
##[8]
D. S. Kim, T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. (Ruse), 7 (2013), 5969-5976
##[9]
T. Kim, D. S. Kim, A Note on Nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88-92
##[10]
D. S. Kim, T. Kim, H. I. Kwon, T. Mansour, Powers under umbral composition and degeneration for Sheffer sequences, Adv. Difference Equ., 2016 (2016), 1-11
##[11]
D. S. Kim, T. Kim, S. H. Lee, J. J. Seo, A note on the lambda-Daehee polynomials, Int. J. Math. Anal. (Ruse), 7 (2013), 3069-3080
##[12]
T. Kim, Y. Simsek, Analytic continuation of the multiple Daehee q-l-functions associated with Daehee numbers, Russ. J. Math. Phys., 15 (2008), 58-65
##[13]
H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q -Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp. Math. (Kyungshang), 18 (2009), 41-48
##[14]
J. W. Park, On the q-analogue of \(\lambda\)-Daehee polynomials, J. Comput. Anal. Appl., 19 (2015), 966-974
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J. W. Park, S. H. Rim, J. Kwon, The twisted Daehee numbers and polynomials, Adv. Difference Equ., 2014 (2014), 1-9
##[16]
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##[17]
J. J. Seo, S. H. Rim, T. Kim, S. H. Lee, Sums products of generalized Daehee numbers, Proc. Jangjeon Math. Soc., 17 (2014), 1-9
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]
Common fixed point theorems in \(C^*\)-algebra-valued metric spaces
Common fixed point theorems in \(C^*\)-algebra-valued metric spaces
en
en
In this paper, we establish coincidence fixed point and common fixed point theorems for two mappings
in complete \(C^*\)-algebra-valued metric spaces which satisfy new contractive conditions. Some applications of
our obtained results are given.
4617
4627
Qiaoling
Xin
School of Mathematical Sciences
School of Mathematics and Statistics
Tianjin Normal University
Beijing Institute of Technology
P. R. China
P. R. China
xinqiaoling0923@163.com
Lining
Jiang
School of Mathematics and Statistics
Beijing Institute of Technology
P. R. China
jianglining@bit.edu.cn
Zhenhua
Ma
School of Mathematics and Statistics
Department of Mathematics
Beijing Institute of Technology
Institute of Architecture Civil Engineering
P. R. China
P. R. China
mazhenghua_1981@163.com
Common fixed point
\(C^*\)-algebra
weakly compatible
coincidence point.
Article.100.pdf
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[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420
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A. Amini-Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal., 72 (2010), 2238-2242
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V. Berinde, A common fixed point theorem for compatible quasi contractive self mappings in metric spaces, Appl. Math. Comput., 213 (2009), 348-354
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Y. J. Cho, R. Saadati, S. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl., 61 (2011), 1254-1260
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B. S. Choudhury, N. Metiya, The point of coincidence and common fixed point for a pair of mappings in cone metric spaces, Comput. Math. Appl., 60 (2010), 1686-1695
##[7]
L. Ćirić, B. Samet, H. Aydi, C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406
##[8]
J. Esmaily, S. M. Vaezpour, B. E. Rhoades, Coincidence point theorem for generalized weakly contractions in ordered metric spaces, Appl. Math. Comput., 219 (2012), 1536-1548
##[9]
J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197
##[10]
L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
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S. Janković, Z. Golubović, S. Radenović, Compatible and weakly compatible mappings in cone metric spaces, Math. Comput. Model., 52 (2010), 1728-1738
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G. Jungck, Commuting mappings and common fixed points, Amer. Math. Monthly, 73 (1966), 735-738
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G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771-779
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G. Jungck, S. Radenović, S. Radojević, V. Rakočević, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory and Appl., 2009 (2009), 1-13
##[15]
A. Kumar, S. Rathee, Fixed point and common fixed point results in cone metric space and application to invariant approximation, Fixed Point Theory and Appl., 2015 (2015), 1-17
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Z. H. Ma, L. N. Jiang, H. Sun, \(C^*\)-algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory and Appl., 2014 (2014), 1-11
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G. J. Murphy, \(C^*\)-algebras and operator theory, Academic Press, London (1990)
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S. Rathee, A. Kumar, Some common fixed-point and invariant approximation results with generalized almost contractions, Fixed Point Theory and Appl., 2014 (2014), 1-16
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W. Shatanawi, M. Postolache, Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory and Appl., 2013 (2013), 1-16
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K. Sitthikul, S. Saejung, Common fixed points of Caristi's type mappings via w-distance, Fixed Point Theory and Appl., 2015 (2015), 1-14
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E. Tarafdar, An approach to fixed-point theorems on uniform spaces, Trans. Amer. Math. Soc., 191 (1974), 209-225
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Q. L. Xin, L. N. Jiang, Common fixed point theorems for generalized k-ordered contractions and B-contractions on noncommutative Banach spaces, Fixed Point Theory and Appl., 2015 (2015), 1-11
]
Positive solutions for an impulsive boundary value problem with Caputo fractional derivative
Positive solutions for an impulsive boundary value problem with Caputo fractional derivative
en
en
In this work we use fixed point theorem method to discuss the existence of positive solutions for the
impulsive boundary value problem with Caputo fractional derivative
\[
\begin{cases}
^cD^q_t u(t)=f(t,u(t)),\,\,\,\,\, \texttt{a.e.} t\in [0,1];\\
\Delta u(t_k)=I_k(u(t_k)), \Delta u'(t_k)=J_k(u(t_k)),\,\,\,\,\, k=1,2,...,m;\\
au(0)-bu(1)=0,\quad au'(0)-bu'(1)=0,
\end{cases}
\]
where \(q \in (1; 2)\) is a real number, \(a; b\) are real constants with \(a > b > 0\), and \(^cD^q_t\)
is the Caputo's fractional
derivative of order \(q, f : [0; 1] \times \mathbb{R}^+ \rightarrow \mathbb{R}^+\) and \(I_k; J_k : \mathbb{R}^+ \rightarrow \mathbb{R}^+\) are continuous functions, \(k = 1; 2; ... ;m,
\mathbb{R}^+ := [0;+1)\).
4628
4638
Keyu
Zhang
School of Mathematics
Department of Mathematics
Shandong University
Qilu Normal University
P. R. China
P. R. China
keyu_292@163.com
Jiafa
Xu
School of Mathematical Sciences
Chongqing Normal University
P. R. China
xujiafa292@sina.com
Caputo fractional derivative
impulsive boundary value problem
fixed point theorem
positive solution.
Article.101.pdf
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[1]
B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Anal. Hybrid Syst., 3 (2009), 251-258
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B. Ahmad, S. Sivasundaram, Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Anal. Hybrid Syst., 4 (2010), 134-141
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A. Anguraj, M. Kasthuri, P. Karthikeyan, Integral boundary value problems for fractional impulsive integro differential equations in Banach spaces, Int. J. Anal. Appl., 4 (2014), 56-67
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A. Bouzaroura, S. Mazouzi, Existence results for certain multi-orders impulsive fractional boundary value problem, Results Math., 66 (2014), 1-20
##[5]
Y. Chen, Z. Lv, Z. Xu, Solvability for an impulsive fractional multi-point boundary value problem at resonance, Bound. Value Probl., 2014 (2014), 1-14
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L. Hu, L. Liu, Y. Wu, Positive solutions of nonlinear singular two-point boundary value problems for second-order impulsive differential equations, Appl. Math. Comput., 196 (2008), 550-562
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X. Li, F. Chen, X. Li, Generalized anti-periodic boundary value problems of impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 28-41
##[10]
X. Liu, M. Jia, Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations, Math. Methods Appl. Sci., 39 (2016), 475-487
##[11]
Z. Liu, X. Li, Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 1362-1373
##[12]
I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Academic Press, San Diego - New York - London (1999)
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H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science, Amsterdam (2006)
##[14]
G. Wang, B. Ahmad, L. Zhang, Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions, Comput. Math. Appl., 62 (2011), 1389-1397
##[15]
G.Wang, B. Ahmad, L. Zhang, Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Anal., 74 (2011), 792-804
##[16]
W. Wang, X. Fu, X. Yang, Positive solutions of periodic boundary value problems for impulsive differential equations, Comput. Math. Appl., 58 (2009), 1623-1630
##[17]
X. Zhang, L. Liu, Y. Wu, Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives, Appl. Math. Comput., 219 (2012), 1420-1433
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X. Zhang, L. Liu, Y. Wu, B. Wiwatanapataphee, The spectral analysis for a singular fractional differential equation with a signed measure, Appl. Math. Comput., 257 (2015), 252-263
##[19]
X. Zhang, Y. Wu, L. Caccetta, Nonlocal fractional order differential equations with changing-sign singular perturbation, Appl. Math. Model., 39 (2015), 6543-6552
##[20]
K. Zhang, J. Xu, W. Dong, Positive solutions for a fourth-order p-Laplacian boundary value problem with impulsive effects, Bound. Value Probl., 2013 (2013), 1-12
##[21]
K. Zhao, Multiple positive solutions of integral BVPs for high-order nonlinear fractional differential equations with impulses and distributed delays, Dyn. Syst., 30 (2015), 208-223
##[22]
K. Zhao, P. Gong, Positive solutions for impulsive fractional differential equations with generalized periodic boundary value conditions, Adv. Dierence Equ., 2014 (2014), 1-19
##[23]
J. Zhou, M. Feng, Green's function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application, Bound. Value Probl., 2014 (2014), 1-21
]
Existence and multiplicity of solutions for nonlinear fractional differential equations
Existence and multiplicity of solutions for nonlinear fractional differential equations
en
en
In this paper, we consider the following fractional initial value problems:
\[D^\alpha u(t) = f(t; u(t);D^\beta u(t)); t \in (0; 1];\]
\[u^{(k)}(0) = \eta_k; k = 0; 1; ...; n - 1;\]
where \(n - 1 < \beta < \alpha < n; (n \in N)\) are real numbers, \(D^\alpha\) and \(D^\beta\) are the Caputo fractional derivatives and
\(f \in C([0; 1] \times R)\). Using the fixed point index theory, we study the existence and multiplicity of positive
solutions and obtain some new results.
4639
4646
Hamidreza
Marasi
Department of Mathematical sciences, Basic Science Faculty
Bonab University
Iran
Hamidreza.marasi@gmail.com
Hossein
Piri
Department of Mathematical sciences, Basic Science Faculty
Bonab University
Iran
piri1979@yahoo.com
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Fractional differential equation
positive solution
index fixed point theorem.
Article.102.pdf
[
[1]
T. Chen, W. Liu, Z. Hu, A boundary value problem for fractional differential equation with P-Laplacian operator at resonance, Nonlinear Anal., 75 (2012), 3210-3217
##[2]
J. Deng, Z. Deng, Existence of solutions of initial value problems for nonlinear fractional differential equations, Appl. Math. Lett., 32 (2014), 6-12
##[3]
J. Deng, L. Ma, Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations, Appl. Math. Lett., 23 (2010), 676-680
##[4]
D. J. Gou, V. Lakshmikantham, Nonlinear problems in abstract cones, Academic Press, San Diego (1988)
##[5]
Z. Han, H. Lu, C. Zhang, Positive solutions for eigenvalue problems of fractional differential equation with generalized P-Laplacian, Appl. Math. Comput., 257 (2015), 526-536
##[6]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam (2006)
##[7]
N. Kosmatov, Integral equations and initial value problems for nonlinear differential equations of fractional order, Nonlinear Anal., 70 (2009), 2521-2529
##[8]
S. Liang, J. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Nonlinear Anal., 71 (2009), 5545-5550
##[9]
H. R. Marasi, H. Afshari, C. B. Zhai, Some existence and uniqueness results for nonlinear fractional partial differential equations, Rocky Mountain J. Math., ((To appear)), -
##[10]
K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley & Sons, New York (1993)
##[11]
I. Podlubny, Fractional differential equations, Academic Press, San Diego (1999)
##[12]
Y. Sun, Positive solutions of Sturm-Liouville boundary value problems for singular nonlinear second-order impulsive integro-differential equation in Banach spaces, Bound. Value Probl., 2012 (2012), 1-18
##[13]
X. Zhang, L. Wang, Q. Sun, Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter, Appl. Math. Comput., 226 (2014), 708-718
]
Extension of Furuta inequality with nonnegative powers for multi-operator
Extension of Furuta inequality with nonnegative powers for multi-operator
en
en
We prove an extension of Furuta inequality with nonnegative powers for multi-operator. Then we show
its application to Pedersen-Takesaki type operator equation.
4647
4650
Jian
Shi
College of Mathematics and Information Science
Hebei University
China
mathematic@126.com
Junmin
Han
School of Mathematics and Information Science
Weifang University
China
goodlucktotoro@126.com
Furuta inequality and Furuta type inequality
positive operators and strictly positive operators
Pedersen-Takesaki operator equation.
Article.103.pdf
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[1]
R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc., 17 (1966), 413-415
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T. Furuta, \( A \geq B \geq 0\) ensures \((B^rA^pB^r)\frac{1}{q} \geq B^{\frac{(p+2r)}{q}}\) for \(r \geq 0; p \geq 0; q \geq 1\) with \((1 + 2r)q \geq p + 2r\), Proc. Amer. Math. Soc., 101 (1987), 85-88
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C. Yang, Y. Wang, Further extension of Furuta inequality, J. Math. Inequal., 4 (2010), 391-398
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C. Yuan, G. Ji, Extensions of Kadison's inequality on positive linear maps, Linear Algebra Appl., 436 (2012), 747-752
]
On fixed points of (\(\eta,\theta\))-quasicontraction mappings in generalized metric spaces
On fixed points of (\(\eta,\theta\))-quasicontraction mappings in generalized metric spaces
en
en
We establish some fixed point results for mappings satisfying (\(\eta,\theta\))-quasicontraction condition in complete generalized metric spaces. Our results generalize many others. An example is provided to support our
work.
4651
4658
Habes
Alsamir
School of mathematical Sciences, Faculty of Science and Technology
University Kebangsaan Malaysia
Malaysia
h.alsamer@gmail.com
Mohd Salmi MD
Noorani
School of mathematical Sciences, Faculty of Science and Technology
University Kebangsaan Malaysia
Malaysia
msn@ukm.my
Wasfi
Shatanawi
Department of Mathematics
Department of Mathematics and general courses
Hashemite University
Prince Sultan University
Jordan
Saudi Arabia
wshatanawi@yahoo.com;wshatanawi@psu.edu.sa
(\(\eta،\theta\))-quasicontraction mappings
(\(\eta،\theta\))-contraction mappings
complete generalized metric spaces.
Article.104.pdf
[
[1]
S. M. Abusalim, M. S. M. Noorani, Fixed point and common fixed point theorems on ordered cone b-metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-7
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R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116
##[3]
H. Aydi, M. Abbas, W. Sintunavarat, P. Kumam, Tripled fixed point of W-compatible mappings in abstract metric spaces, Fixed Point Theory and Appl., 2012 (2012), 1-20
##[4]
H. Aydi, M. Postolache, W. Shatanawi, Coupled fixed point results for (\(\psi,\phi\))-weakly contractive mappings in ordered G-metric spaces, Comput. Math. Appl., 63 (2012), 298-309
##[5]
H. Aydi, W. Shatanawi, C. Vetro, On generalized weak G-contraction mapping in G-metric spaces, Comput. Math. Appl., 62 (2011), 4223-4229
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I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ul'yanovsk. Gos. Ped. Inst., Ul'yanovsk, 30 (1989), 26-37
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
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N. Bilgili, E. Karapinar, B. Samet, Generalized \(\alpha-\psi\) contractive mappings in quasi-metric spaces and related fixed-point theorems, J. Inequal. Appl., 2014 (2014), 1-15
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M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377
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Dislocated topologies, P. Hitzler, A. Seda, J. Electr. Eng., 51 (2000), 3-7
##[11]
M. Jleli, B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory and Appl., 2015 (2015), 1-14
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Z. Mustafa, M. Khandaqji, W. Shatanawi, Fixed point results on complete G-metric spaces, Studia Sci. Math. Hungar., 48 (2011), 304-319
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H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen Co., Tokyo (1950)
##[16]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equation, Acta Math. Sin., 23 (2007), 2205-2212
##[17]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443
##[18]
W. Shatanawi, M. Postolache, Common fixed point results for mappings under nonlinear contraction of cyclic form in ordered metric spaces, Fixed Point Theory and Appl., 2013 (2013), 1-13
]
Generalized contraction mapping principle in locally convex topological vector spaces
Generalized contraction mapping principle in locally convex topological vector spaces
en
en
The purpose of this paper is to present the concept of contraction mapping in a locally convex topological
vector spaces and to prove the generalized contraction mapping principle in such spaces. The neighborhood-
type error estimate formula was also established. The results of this paper improve and extend Banach
contraction mapping principle in new idea.
4659
4665
Yanxia
Tang
Department of Mathematics
Hebei North University
P. R. China
tyx402@126.com
Jinyu
Guan
Department of Mathematics
Hebei North University
P. R. China
guanjinyu2010@163.com
Pengcheng
Ma
Department of Mathematics
Hebei North University
P. R. China
mapengcheng@163.com
Yongchun
Xu
Department of Mathematics
Hebei North University
P. R. China
hbxuyongchun@163.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
P. R. China
tjsuyongfu@163.com
Contraction mapping principle
locally convex
topological vector spaces
fixed point
error estimate formula.
Article.105.pdf
[
[1]
A. Amini-Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal., 72 (2010), 2238-2242
##[2]
D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458-464
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##[5]
T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
##[6]
J. Harjani, K. Sadarangni, Fixed point theorems for weakly contraction mappings in partially ordered sets, Non- linear Anal., 71 (2009), 3403-3410
##[7]
J. Harjani, K. Sadarangni, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197
##[8]
J. R. Jachymski, Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., 125 (1997), 2327-2335
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J. Jachymski, I. Jóźwik, Nonlinear contractive conditions: a comparison and related problems, n: Fixed Point Theory and its Applications, Polish Acad. Sci., Banach Center Publ., 77 (2007), 123-146
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M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9
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V. Lakshmikantham, L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
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J. J. Nieto, R. Rodriguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
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J. J. Nieto, R. Rodriguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin., 23 (2007), 2205-2212
##[14]
D. O'Regan, A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241-1252
##[15]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contactive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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Y. Su, A. Petruşel, J. C. Yao, Multivariate fixed point theorems for contractions and nonexpansive mappings with applications, Fixed Point Theory and Appl., 2016 (2016), 1-9
##[17]
Y. Su, J. C. Yao, Further generalized contraction mapping principle and best proximity theorem in metric spaces, Fixed Point Theory and Appl., 2015 (2015), 1-13
##[18]
F. Yan, Y. Su, Q. Feng, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory and Appl., 2012 (2012), 1-13
]
Dual synchronization of chaotic and hyperchaotic systems
Dual synchronization of chaotic and hyperchaotic systems
en
en
The existence of the dual synchronization behavior between a pair of chaotic and hyperchaotic systems is
investigated via a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear
feedback term. The sufficient conditions for achieving the dual synchronization behavior between a pair of
chaotic and hyperchaotic systems using a nonlinear feedback controller are derived by using the Lyapunov
stability theorem. The dual synchronization behavior between a pair of chaotic systems (Chen and Lorenz
system) and a pair of hyperchaotic systems hyperchaotic Chen system and hyperchaotic Lü system are
taken as two illustrative examples to show the effectiveness of the proposed method. Theoretical analysis
and numerical simulations are performed to verify the results.
4666
4677
A. Almatroud
Othman
School of Mathematical Sciences
Universiti Kebangsaan Malaysia
Malaysia
othman almatroud@yahoo.com
M. S. M.
Noorani
School of Mathematical Sciences
Universiti Kebangsaan Malaysia
Malaysia
msn@ukm.my
M. Mossa
Al-Sawalha
Mathematics Department, Faculty of Science
University of Hail
Kingdom of Saudi Arabia
sawalha_moh@yahoo.com
Dual synchronization
chaos
hyperchaos
lyapunov stability theory.
Article.106.pdf
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[1]
G. Chen, X. Dong, From chaos to order, methodologies, perspectives and applications, World Scientific Publishing Co., River Edge, NJ (1998)
##[2]
A. Chen, J. Lu, J. Lü, S. Yu, Generating hyperchaotic Lü attractor via state feedback control, Phys. A, 364 (2006), 103-110
##[3]
H. H. Chen, G. J. Sheu, Y. L. Lin, C. S. Chen, Chaos synchronization between two different chaotic systems via nonlinear feedback control, Nonlinear Anal., 70 (2009), 4393-4401
##[4]
G. Chen, T. Ueta, Yet another chaotic attractor, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 9 (1999), 1465-1476
##[5]
C. F. Feng, Projective synchronization between two different time-delayed chaotic systems using active control approach, Nonlinear Dyn., 62 (2010), 453-459
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D. Ghosh, Projective-dual synchronization in delay dynamical systems with time-varying coupling delay, Nonlinear Anal., 66 (2011), 717-730
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D. Ghosh, R. A. Chowdhury, Dual-anticipating, dual and dual-lag synchronization in modulated time-delayed systems, Phys. Lett. A, 374 (2010), 3425-3436
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J. La Salle, S. Lefschetz, Stability by Liapunov's direct method, with applications, Academic Press, New York (1961)
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Y. T. A. Leung, X. F. Li, Y. D. Chu, X. B. Rao, A simple adaptive-feedback scheme for identical synchronizing chaotic systems with uncertain parameters, Appl. Math. Comput., 253 (2015), 172-183
##[10]
W. Li, Z. Liu, J. Miao, Adaptive synchronization for a unified chaotic system with uncertainty, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 3015-3021
##[11]
Y. Li, W. K. Tang, G. Chen, Generating hyperchaos via state feedback control, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 15 (2005), 3367-3375
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Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control
Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control
en
en
In this paper, the problem of the lag synchronization between two general complex dynamical networks
with mixed coupling by pinning control is studied. Based on the Lyaponov functional theory and mathematical
analysis method, less conservative conditions of lag synchronization are obtained by adding the
controllers to part of nodes. Moreover, the coupling configuration matrices are not required to be symmetric
or irreducible. It is shown that the lag synchronization of the drive and response systems can be realized
via the linear feedback pinning control and adaptive feedback pinning control. These results remove some
restrictions on the node dynamics and the number of the pinned nodes. Numerical examples are presented
to illustrate the effectiveness of the theoretical results.
4678
4694
Xiaojun
Zhang
School of Mathematics Sciences
University of Electronic Science and Technology of China
P. R. China
sczhxj@uestc.edu.cn
Huilan
Yang
School of Mathematics Sciences
University of Electronic Science and Technology of China
P. R. China
Shouming
Zhong
School of Mathematics Sciences
University of Electronic Science and Technology of China
P. R. China
Lag synchronization
complex dynamical systems
pinning control
hybrid time-varying
Article.107.pdf
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]
On the extended multivalued Geraghty type contractions
On the extended multivalued Geraghty type contractions
en
en
In this paper we present some absolute retract results for modified Geraghty multivalued type contractions in b-metric space. Our results, generalize several existing results in the corresponding literature. We
also present some examples to support the obtained results.
4695
4706
Hojjat
Afshari
Faculty of Basic Science
University of Bonab
Iran
hojat.afshari@yahoo.com;hojat.afshari@bonabu.ac.ir
Hamed H.
Alsulami
Nonlinear Analysis and Applied Mathematics Research Group (NAAM)
King Abdulaziz University
Saudi Arabia
hamed9@hotmail.com;hhaalsalmi@kau.edu.sa
Erdal
Karapinar
Department of Mathematics
Atilim University
Turkey
erdalkarapinar@yahoo.com;erdal.karapinar@atilim.edu.tr
Fixed points
extended multivalued Geraghty type contractions.
Article.108.pdf
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]
Some identities of degenerate \(q\)-Euler polynomials under the symmetry group of degree \(n\)
Some identities of degenerate \(q\)-Euler polynomials under the symmetry group of degree \(n\)
en
en
In this paper, we derive some interesting identities of symmetry for the degenerate q-Euler polynomials
under the symmetry group of degree n arising from the fermionic p-adic q-integral on \(\mathbb{Z}_p\).
4707
4712
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
D. V.
Dolgy
Hanrimwon
Institute of Natural Sciences
Kwangwoon University
Far eastern Federal University
Republic of Korea
Russia
d_dol@mail.ru
Lee-Chae
Jang
Graduate School of Education
Konkuk University
Republic of Korea
lcjang@konkuk.ac.kr
Hyuck-In
Kwon
Department of Mathematics
Kwangwoon University
Republic of Korea
sura@kw.ac.kr
Identities of symmetry
degenerate q-Euler polynomial
symmetry group of degree n
fermionic p-adic q-integral.
Article.109.pdf
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[1]
L. Carlitz, q-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc., 76 (1954), 332-350
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D. V. Dolgy, T. Kim, H. I. Kwon, J. J. Seo, Symmetric identities of degenerate q-Bernoulli polynomials under symmetry group \(S_3\), Proc. Jangjeon Math. Soc., 19 (2016), 1-9
##[4]
Y. He, Symmetric identities for Carlitz's q-Bernoulli numbers and polynomials, Adv. Difference Equ., 2013 (2013), 1-10
##[5]
T. Kim, Symmetry p-adic invariant integral on \(\mathbb{Z}_p\) for Bernoulli and Euler polynomials, J. Difference Equ. Appl., 14 (2008), 1267-1277
##[6]
T. Kim, Some identities on the q-Euler polynomials of higher-order and q-Stirling numbers by the fermionic p-adic integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 484-491
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T. Kim, Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 93-96
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T. Kim, New approach to q-Euler polynomials of higher-order, Russ. J. Math. phys., 17 (2010), 218-225
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T. Kim, D. V. Dolgy, J. J. Seo, Identities of symmetry for degenerate q-Euler polynomials, Adv. Stud. Contemp. Math., 25 (2015), 577-582
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Y. H. Kim, K. W. Hwang, Symmetry of power sum and twisted Bernoulli polynomials, Adv. Stud. Contemp. Math., 18 (2009), 127-133
##[12]
D. S. Kim, T. Kim, Some identities of degenerate Euler polynomials arising from p-adic fermionic integral on \(\mathbb{Z}_p\), Integral Transforms Spec. Funct., 26 (2015), 295-302
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D. S. Kim, T. Kim, Symmetric identities of higher-order degenerate q-Euler polynomials, J. Nonlinear Sci. Appl., 9 (2016), 443-451
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D. S. Kim, T. Kim, Symmetry identities of higher-order q-Euler polynomials under the symmetric group of degree four, J. Comput. Anal. Appl., 21 (2016), 521-527
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T. Kim, H. I. Kwon, J. J. Seo, Identities of symmetry for degenerate q-Bernoulli polynomials, Proc. Jangjeon Math. Soc., 18 (2015), 495-499
##[17]
D. S. Kim, N. Lee, J. Na, K. H. Park, Identities of symmetry for higher-order Euler polynomials in three variables (I), Adv. Stud Contemp. Math., 22 (2012), 51-74
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##[19]
H. I. Kwon, T. Kim, J. J. Seo, Some identities of symmetry for modified degenerate Frobenius-Euler polynomials, Adv. Stud. Contemp. Math., 26 (2016), 299-305
##[20]
E. J. Moon, S. H. Rim, J. H. Jin, S. J. Lee, On the symmetric properties of higher-order twisted q-Euler numbers and polynomials, Adv. Difference Equ., 2010 (2010), 1-8
]
Stability of higher-order nonlinear impulsive differential equations
Stability of higher-order nonlinear impulsive differential equations
en
en
For a higher-order nonlinear impulsive ordinary differential equation, we present the concepts of Hyers-
Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam{Rassias stability, and generalized Hyers-
Ulam-Rassias stability. Furthermore, we prove the generalized Hyers-Ulam-Rassias stability by using integral
inequality of Grönwall type for piecewise continuous functions. These results extend related contributions
to the corresponding first-order impulsive ordinary differential equation. Hyers-Ulam stability,
generalized Hyers-Ulam stability, and Hyers-Ulam-Rassias stability can be discussed by the same methods.
4713
4721
Shuhong
Tang
School of Information and Control Engineering
Weifang University
P. R. China
wfxytang@163.com
Akbar
Zada
Department of Mathematics
University of Peshawar
Pakistan
zadababo@yahoo.com
Shah
Faisal
Department of Mathematics
University of Peshawar
Pakistan
shahfaisal8763@gmail.com
M. M. A.
El-Sheikh
Department of Mathematics, Faculty of Science
Menoufia University
Egypt
msheikh_1999@yahoo.com
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Informatics
Linyi University, Linyi
Linyi University
P. R. China
P. R. China
litongx2007@163.com
Hyers-Ulam stability
generalized Hyers-Ulam stability
Hyers-Ulam-Rassias stability
generalized Hyers-Ulam-Rassias stability
nonlinear impulsive differential equation
higher-order
Grönwall inequality.
Article.110.pdf
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C. Parthasarathy, Existence and Hyers-Ulam stability of nonlinear impulsive differential equations with nonlocal conditions,, Electron. J. Math. Anal. Appl., 4 (2016), 106-115
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D. Popa, I. Raşa, Hyers-Ulam stability of the linear differential operator with nonconstant coefficients, Appl. Math. Comput., 219 (2012), 1562-1568
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S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York-London (1960)
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J. R. Wang, M. Fečkan, Y. Zhou, Ulam's type stability of impulsive ordinary differential equations, J. Math. Anal. Appl., 395 (2012), 258-264
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P. Wang, X. Liu, \(\phi_0\)-Stability of hybrid impulsive dynamic systems on time scales, J. Math. Anal. Appl., 334 (2007), 1220-1231
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P. Wang, M. Wu, Practical \(\phi_0\)-stability of impulsive dynamic systems on time scales, Appl. Math. Lett., 20 (2007), 651-658
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L. Wang, B. Yang, A. Abraham, Distilling middle-age cement hydration kinetics from observed data using phased hybrid evolution, Soft Comput., 20 (2016), 3637-3656
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L. Wang, B. Yang, Y. Chen, X. Zhang, J. Orchard, Improving neural-network classifiers using nearest neighbor partitioning, IEEE Trans. Neural Netw. Learn. Syst., ((In press)), -
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L. Wang, B. Yang, J. Orchard, Particle swarm optimization using dynamic tournament topology, Appl. Soft Comput., 48 (2016), 584-596
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A. Zada, S. Faisal, Y. Li, On the Hyers-Ulam stability of first-order impulsive delay differential equations, J. Funct. Spaces, 2016 (2016), 1-6
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]
Certain new summation formulas for the series \(_4F_3 (1)\) with applications
Certain new summation formulas for the series \(_4F_3 (1)\) with applications
en
en
The main objective of this paper is to provide thirteen (presumably) new summation formulas for
the series \(_4F_3\) of unit argument expressed in terms of Gamma functions. As special cases of our main
results, we also present twenty four summation formulas for the terminating \(_4F_3 (1)\), whose further special
cases are derived to give thirty two known summation formulas for the terminating \(_4F_3 (1)\). The results
presented here are established with the help of a general result recorded in the book of Prudnikov et al.
and the generalization of Watson's summation theorem obtained earlier by Lavoie et al.
4722
4736
Junesang
Choi
Department of Mathematics
Dongguk University
Republic of Korea
junesang@mail.dongguk.ac.kr
Arjun K.
Rathie
Department of Mathematics, School of Mathematical and Physical Sciences
Central University of Kerala, Riverside Transit Campus
India
akrathie@gmail.com
Gamma function
Pochhammer symbol
generalized hypergeometric function
Watson's summation theorem
generalized Watson's summation theorem.
Article.111.pdf
[
[1]
W. N. Bailey, Generalized hypergeometric series, Cambridge University Press, Cambridge (1935)
##[2]
Y. S. Kim, S. Gaboury, A. K. Rathie, Two results for a special \(_4F_3\), (submitted), (), -
##[3]
Y. S. Kim, M. A. Rakha, A. K. Rathie, Extensions of certain classical summation theorems for the series \(_2F_1, _3F_2\) and \(_4F_3\) with applications in Ramanujan's summations, Int. J. Math. Math. Sci., 2010 (2010), 1-26
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Some fixed point results of multi-valued nonlinear \(F\)-contractions without the Hausdorff metric
Some fixed point results of multi-valued nonlinear \(F\)-contractions without the Hausdorff metric
en
en
Fixed point results for several multi-valued nonlinear F-contractions without the Hausdorff metric are
given and three examples are included. The results obtained in this paper differ from the corresponding
results in the literature.
4737
4753
Zeqing
Liu
Department of Mathematics
Liaoning Normal University
People's Republic of China
zeqingliu@163.com
Xue
Na
Department of Mathematics
Liaoning Normal University
People's Republic of China
xuena08@163.com
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
Korea
ooly61@yahoo.co.kr
Multi-valued nonlinear F-contraction
fixed point
iterative approximation.
Article.112.pdf
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Best proximity and coupled best proximity results for Suzuki type proximal multivalued mappings
Best proximity and coupled best proximity results for Suzuki type proximal multivalued mappings
en
en
We extend and generalize the best proximity results for Suzuki type \(\alpha^+-\psi\)-proximal single valued mappings given by Hussain et al. Some novel best proximity results and coupled best proximity results are
presented for Suzuki type \(\alpha^+-\psi\)-proximal multivalued mappings satisfying generalized conditions of existence.
4754
4771
Xuelian
Xu
School of Mathematical Sciences
Harbin Normal University
P. R. China
xuelian632@163.com
Xiaoming
Fan
School of Mathematical Sciences
Harbin Normal University
P. R. China
fanxm093@163.com
Haiming
Liu
School of Mathematics
Mudanjiang Normal University
P. R. China
liuhm468@nenu.edu.cn
Suzuki type \(\alpha^+-\psi\)-proximal multivalued mappings
coupled best proximity point
best proximity point.
Article.113.pdf
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N. Hussain, A. Latif, P. Salimi, Best proximity point results for modified Suzuki \(\alpha-\psi\)-proximal contractions, Fixed Point Theory and Appl., 2014 (2014), 1-16
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]
A hybrid algorithm with Meir-Keeler contraction for asymptotically pseudocontractive mappings
A hybrid algorithm with Meir-Keeler contraction for asymptotically pseudocontractive mappings
en
en
A hybrid algorithm with Meir-Keeler contraction for finding the fixed points of the asymptotically
pseudocontractive mappings is presented. Some strong convergence results are given.
4772
4779
Youli
Yu
School of Mathematics and Information Engineering
Taizhou University
China
yuyouli@tzc.edu.cn
Ching-Feng
Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University, Kaohsiung
Taiwan
cfwen@kmu.edu.tw
Xiaoyin
Wang
Department of Mathematics
Tianjin Polytechnic University
China
wxywxq@163.com
Asymptotically pseudocontractive mapping
hybrid algorithm
fixed point.
Article.114.pdf
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[1]
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H. Zegeye, N. Shahzad, An algorithm for a common fixed point of a family of pseudocontractive mappings, Fixed Point Theory and Appl., 2013 (2013), 1-14
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H. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 3140-3145
]
General convolution identities for Apostol-Bernoulli, Euler and Genocchi polynomials
General convolution identities for Apostol-Bernoulli, Euler and Genocchi polynomials
en
en
We perform a further investigation for the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. By making use of the generating function methods and summation transform techniques, we establish some general convolution identities for the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi
polynomials. These results are the corresponding extensions of some known formulas including the general
convolution identities discovered by Dilcher and Vignat [K. Dilcher, C. Vignat, J. Math. Anal. Appl., 435
(2016), 1478-1498] on the classical Bernoulli and Euler polynomials.
4780
4797
Yuan
He
Faculty of Science
Kunming University of Science and Technology
P. R. China
hyyhe@aliyun.com;hyyhe@outlook.com
Taekyun
Kim
Department of Mathematics
Kwangwoon University
Korea
tkkim@kw.ac.kr
Apostol-Bernoulli polynomials and numbers
Apostol-Euler polynomials and numbers
Apostol-Genocchi polynomials and numbers
combinatorial identities.
Article.115.pdf
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[1]
T. Agoh, Convolution identities for Bernoulli and Genocchi polynomials, Electron. J. Combin., 21 (2014), 1-14
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T. Agoh, K. Dilcher, Convolution identities and lacunary recurrences for Bernoulli numbers, J. Number Theory, 124 (2007), 105-122
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T. Agoh, K. Dilcher, Higher-order recurrences for Bernoulli numbers, J. Number Theory, 129 (2009), 1837-1847
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]
Hybrid shrinking iterative solutions to convex feasibility problems and a system of generalized mixed equilibrium problems
Hybrid shrinking iterative solutions to convex feasibility problems and a system of generalized mixed equilibrium problems
en
en
The purpose of this paper is to propose a new hybrid shrinking iterative scheme for approximating
common elements of the set of solutions to convex feasibility problems for countable families of weak relatively
nonexpansive mappings of a set of solutions to a system of generalized mixed equilibrium problems. A strong
convergence theorem is established in the framework of Banach spaces. The results extend those of other
authors, in which the involved mappings consist of just finitely many ones.
4798
4813
Youbing
Xiong
Department of Mathematics, School of Science
Tianjin University
P. R. China
xyb314@sina.com
Weak relatively nonexpansive mappings
relatively nonexpansive mappings
hybrid iteration scheme
convex feasibility problems
generalized mixed equilibrium problems.
Article.116.pdf
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Y. Yao, M. Postolache, Y. C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory and Appl., 2013 (2013), 1-12
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J. Zhang, Y. Su, Q. Cheng, Hybrid algorithm of fixed point for weak relatively nonexpansive multivalued mappings and applications, Abstr. Appl. Anal., 2012 (2012), 1-13
]
Common best proximity results for multivalued proximal contractions in metric space with applications
Common best proximity results for multivalued proximal contractions in metric space with applications
en
en
The study of the best proximity points is an interesting topic of optimization theory. We introduce the
notion of \(\alpha_*\)-proximal contractions for multivalued mappings on a complete metric space and establish the
existence of common best proximity point for these mappings in the context of multivalued and single-valued
mappings. As an application, we derive some best proximity point and fixed point results for multivalued and
single-valued mappings on partially ordered metric spaces. Our results generalize and extend many known
results in the literature. Some examples are provided to illustrate the results obtained herein.
4814
4828
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Abdul Rahim
Khan
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals Dhahran
Saudi Arabia
arahim@kfupm.edu.sa
Iram
Iqbal
Department of Mathematics
University of Sargodha
Pakistan
irami@uos.edu.pk
\(\alpha_*\)-proximal admissible mapping
common best proximity point
multivalued mapping.
Article.117.pdf
[
[1]
M. Abbas, A. Hussain, P. Kumam, A coincidence best proximity point problem in G-metric spaces, Abstr. Appl. Anal., 2015 (2015), 1-12
##[2]
A. Abkar, M. Gabeleh, Best proximity points for cyclic mappings in ordred metric spaces, Optim. Theory Appl., 150 (2011), 188-193
##[3]
A. Abkar, M. Gabeleh, Generalized cyclic contractions in partially ordered metric spaces, Optim. Lett., 6 (2012), 1819-1830
##[4]
A. Abkar, M. Gabeleh, The existence of best proximity points for multivalued non-self-mappings, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 107 (2013), 319-325
##[5]
M. U. Ali, T. Kamram, E. Karapinar, Further discussion on modified multivalued \(\alpha_*-\psi\)-contractive type mapping, Filomat, 29 (2015), 1893-1900
##[6]
M. U. Ali, T. Kamram, N. Shahzad, Best proximity point for \(\alpha-\psi\)-proximal contractive multimaps, Abstr. Appl. Anal., 2014 (2014), 1-6
##[7]
A. Amini-Harandi, Best proximity points for proximal generalized contractions in metric spaces, Optim. Lett., 7 (2013), 913-921
##[8]
A. Amini-Harandi, M. Fakhar, H. R. Hajisharifi, N. Hussain, Some new results on fixed and best proximity points in preordered metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-15
##[9]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
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S. S. Basha, Discrete optimization in partially ordered sets, J. Global Optim., 54 (2012), 511-517
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S. S. Basha, Best proximity point theorems on partially ordered sets, Optim. Lett., 7 (2013), 1035-1043
##[12]
A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006
##[13]
K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 122 (1969), 234-240
##[14]
M. Gabeleh, Best proximity points: global minimization of multivalued non-self mappings, Optim. Lett., 8 (2014), 1101-1112
##[15]
N. Hussain, M. A. Kutbi, P. Salimi, Best proximity point results for modified \(\alpha-\psi\)-proximal rational contractions, Abstr. Appl. Anal., 2013 (2013), 1-14
##[16]
N. Hussain, A. Latif, P. Salimi, Best proximity point results for modified Suzuki \(\alpha-\psi\)-proximal contractions, Fixed Point Theory and Appl., 2014 (2014), 1-16
##[17]
N. Hussain, P. Salimi, A. Latif, Fixed point results for single and set-valued \(\alpha-\eta-\psi\)-contractive mappings, Fixed Point Theory and Appl., 2013 (2013), 1-23
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G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771-779
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G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., 4 (1996), 199-215
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E. Karapınar, Best proximity points of cyclic mappings, Appl. Math. Lett., 25 (2007), 79-92
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A. R. Khan, S. A. Shukri, Best proximity points in the Hilbert ball, J. Nonlinear Convex Anal., ((Accepted)), -
##[22]
A. Latif, M. Hezarjaribi, P. Salimi, N. Hussain, Best proximity point theorems for \(\alpha-\psi\)-proximal contractions in intuitionistic fuzzy metric spaces, J. Inequal. Appl., 2014 (2014), 1-19
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P. Lo'lo', S. M. Vaezpour, J. Esmaily, Common best proximity points theorem for four mappings in metric-type spaces, Fixed Point Theory and Appl., 2015 (2015), 1-7
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S. B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math., 30 (1969), 475-488
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V. Pragadeeswarar, M. Marudai, Best proximity points: approximation and optimization in partially ordered metric spaces, Optim. Lett., 7 (2013), 1883-1892
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V. Pragadeeswarar, M. Marudai, Best proximity points for generalized proximal weak contractions in partially ordered metric spaces, Optim. Lett., 9 (2015), 105-118
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V. Pragadeeswarar, M. Marudai, P. Kumam, Best proximity point theorems for multivalued mappings on partially ordered metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 1911-1921
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P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory and Appl., 2013 (2013), 1-19
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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]
Approximate analytical solutions of Goursat problem within local fractional operators
Approximate analytical solutions of Goursat problem within local fractional operators
en
en
The local fractional differential transform method (LFDTM) and local fractional decomposition method
(LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local
fractional derivative operators. The approximate analytical solution of this problem is calculated in form
of a series with easily computable components. Examples are studied in order to show the accuracy and
reliability of presented methods. We demonstrate that the two approaches are very effective and convenient
for finding the analytical solutions of partial differential equations with local fractional derivative operators.
4829
4837
Dumitru
Baleanu
Department of Mathematics, Faculty of Arts and Sciences
Cankaya University
Turkey
dumitru@cankaya.edu.tr
Hassan Kamil
Jassim
Department of Mathematics, Faculty of Education for Pure Sciences
University of Thi-Qar
Iraq
hassan.kamil28@yahoo.com
Maysaa Al
Qurashi
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
maysaa@ksu.edu.sa
Goursat problem
local fractional differential transform method
local fractional decomposition method
analytical solutions
local fractional derivative operators.
Article.118.pdf
[
[1]
Z. P. Fan, H. K. Jassim, R. K. Rainna, X. J. Yang, Adomian decomposition method for three-dimensional diffusion model in fractal heat transfer involving local fractional derivatives, Thermal Sci., 19 (2015), 137-141
##[2]
H. Jafari, H. K. Jassim, Application of the local fractional Adomian decomposition and series expansion methods for solving telegraph equation on Cantor sets involving local fractional derivative operators, J. Zankoy Sulaimani- Part A, 17 (2015), 15-22
##[3]
S. Q. Wang, Y. J. Yang, H. K. Jassim, Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative, Abstr. Appl. Anal., 2014 (2014), 1-7
##[4]
S. H. Yan, X. H. Chen, G. N. Xie, C. Cattani, X. J. Yang, Solving Fokker-Planck equations on Cantor sets using local fractional decomposition method, Abstr. Appl. Anal., 2014 (2014), 1-6
##[5]
S. P. Yan, H. Jafari, H. K. Jassim, Local fractional Adomian decomposition and function decomposition methods for Laplace equation within local fractional operators, Adv. Math. Phys., 2014 (2014), 1-7
##[6]
X. J. Yang, Advanced local fractional calculus and its applications, World Sci. Publ., New York (2012)
##[7]
X. J. Yang, J. A. Tenreiro Machado, H. M. Srivastava, A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach, Appl. Math. Comput., 274 (2016), 143-151
]
Some common fixed point results of graphs on \(b\)-metric space
Some common fixed point results of graphs on \(b\)-metric space
en
en
The aim of this paper is to present some coincidence point results and common fixed points for pair
of self-mappings satisfying generalized contractive condition in the framework of b-metric spaces endowed
with a graph. We present applications and some examples to illustrate the main result.
4838
4851
Zead
Mustafa
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
zead@qu.edu.qa
M. M. M.
Jaradat
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
mmjst4@qu.edu.qa
H. M.
Jaradat
Department of Mathematics
Department of Mathematics and Applied Sciences
Al al-Bayt University
Dhofar University
Jordan
Oman
husseinjaradat@yahoo.com
Coincidence point
common fixed point with graph
b-metric Space.
Article.119.pdf
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[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric space, J. Math. Anal. Appl., 341 (2008), 416-420
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A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014), 941-960
##[3]
S. Aleomraninejad, S. Rezapour, N. Shahzad, Fixed point results on subgraphs of directed graphs, Math. Sci., 7 (2013), 1-3
##[4]
M. R. Alfuraidan, M. A. Khamsi, Caristi fixed point theorem in metric spaces with a graph, Abstr. Appl. Anal., 2014 (2014), 1-5
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I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, (Russian), Funct. Anal. Gos. Ped. Inst. Unianowsk, 30 (1989), 26-37
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I. Beg, A. R. Butt, S. Radojević, The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60 (2010), 1214-1219
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F. Bojor, Fixed point of \(\phi\)-contraction in metric spaces endowed with a graph, An. Univ. Craiova Ser. Mat. Inform., 37 (2010), 85-92
##[8]
F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. Ştiinţ. Univ. Ovidius Constantá Ser. Mat., 20 (2012), 31-40
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J. A. Bondy, U. S. R. Murty, Graph theory with applications, American Elsevier Publishing Co., Inc., New York (1976)
##[10]
M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Stud. Univ. Babes-Bolyai Math., 54 (2009), 3-14
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M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4 (2009), 285-301
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S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
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S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276
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F. Echenique, A short and constructive proof of Tarski's fixed-point theorem, Internat. J. Game Theory, 33 (2005), 215-218
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R. Espínola, W. A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153 (2006), 1046-1055
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J. L. Gross, J. Yellen, Graph theory and its applications, Discrete Math. Appl., Boca Raton (2006)
##[17]
N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly (\(\psi,\varphi, L, A,B\))-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory and Appl., 2013 (2013), 1-18
##[18]
N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684
##[19]
J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359-1373
##[20]
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261-263
##[21]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771-779
##[22]
G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc., 103 (1988), 977-983
##[23]
G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., 4 (1996), 199-215
##[24]
G. Jungck, N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl., 325 (2007), 1003-1012
##[25]
M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129
##[26]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., 2013 (2013), 1-26
##[27]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Fixed point theorems for weakly T-Chatterjea and weakly T-Kannan contractions in b-metric spaces, J. Inequal. Appl., 2014 (2014), 1-14
##[28]
M. Păcurar, Sequences of almost contractions and fixed points in b-metric spaces, An. Univ. Vest Timis. Ser. Mat.-Inform., 48 (2010), 125-137
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R. P. Pant, Common fixed points of noncommuting mappings, Math. Anal. Appl., 188 (1994), 436-440
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S. Sedghi, N. Shobkolaei, J. R. Roshan, W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik, 66 (2014), 190-201
##[31]
S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.), 32 (1982), 149-153
##[32]
S. L. Singh, B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., 55 (2008), 2512-2520
]
Some results about Krasnosel'skiĭ-Mann iteration process
Some results about Krasnosel'skiĭ-Mann iteration process
en
en
We introduce a Mann type iteration method and give a result about strongly convergence of this iteration
method to a fixed point of nonexpansive mappings on Banach spaces. Also, by using idea of Ishikawa iteration
method, we introduce a new iteration method via two mappings on uniformly convex Banach spaces and
we provide a result about strongly convergence of the iteration method to a common fixed points of the
mappings.
4852
4859
Hojjat
Afshari
Faculty of Basic Science
University of Bonab
Iran
hojat.afshari@yahoo.com;hojat.afshari@bonabu.ac.ir
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Fixed point
Krasnosel'skiĭ-Mann iteration
nonexpansive mapping.
Article.120.pdf
[
[1]
R. P. Agarwal, D. O'Regan, D. R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications, Springer, New York (2009)
##[2]
V. Berinde, n the stability of some fixed point procedures, Bul. Ştiinţ. Univ. Baia Mare Ser. B Fasc. Mat.-Inform., 18 (2002), 7-14
##[3]
V. Berinde, M. Berinde, The fastest Krasnoselskij iteration for approximating fixed points of strictly pseudo- contractive mappings, Carpathian J. Math., 21 (2005), 13-20
##[4]
C. E. Chidume, N. Shahzad, H. Zegeye, Convergence theorems for mappings which are asymptotically nonexpansive in the intermediate sense, Numer. Funct. Anal. Optim., 25 (2004), 239-257
##[5]
W. Q. Deng, A modified Mann iteration process for common fixed points of an infinite family of nonexpansive mappings in Banach spaces, Appl. Math. Sci. (Ruse), 4 (2010), 1521-1526
##[6]
N. Hussain, G. Marino, L. Muglia, B. A. S. Alamri, On some Mann's type iterative algorithms, Fixed Point Theory and Appl., 2015 (2015), 1-16
##[7]
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150
##[8]
S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc., 59 (1976), 65-71
##[9]
T. H. Kim, H. K. Xu, Convergence of the modified Mann's iteration method for asymptotically strict pseudo- contractions, Nonlinear Anal., 68 (2008), 2828-2836
##[10]
M. A. Krasnosel'skiĭ, Two remarks on the method of successive approximations, (Russian) Uspehi Mat. Nauk (N.S.), 10 (1955), 123-127
##[11]
W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510
##[12]
S. Plubtieng, R. Wangkeeree, Strong convergence of modified Mann iterations for a countable family of nonexpansive mappings, Nonlinear Anal., 70 (2009), 3110-3118
##[13]
R. F. Rao, Strong convergence of a modified Mann iteration for a strictly asymptotically pseudocontractive map, (Chinese) Adv. Math. (China), 39 (2010), 283-288
##[14]
Y. Yao, R. Chen, Weak and strong convergence of a modified Mann iteration for asymptotically nonexpansive mappings, Nonlinear Funct. Anal. Appl., 12 (2007), 307-315
]
The extended Srivastavas triple hypergeometric functions and their integral representations
The extended Srivastavas triple hypergeometric functions and their integral representations
en
en
We introduce the extended Srivastava's triple hypergeometric functions by using an extension of beta
function. Furthermore, some integral representations are given for these new functions.
4860
4866
Ayşegül
Çetinkaya
Dept. of Mathematics
Ahi Evran Univ.
Turkey
acetinkaya@ahievran.edu.tr
M. Baki
Yağbasan
Dept. of Mathematics
Ahi Evran Univ.
Turkey
mbakiyag@ahievran.edu.tr
İ. Onur
Kıymaz
Dept. of Mathematics
Ahi Evran Univ.
Turkey
iokiymaz@ahievran.edu.tr
Beta function
Srivastava's triple hypergeometric functions
Appell's hypergeometric function
Exton's function.
Article.121.pdf
[
[1]
M. Bozer, M. A. Özarslan, Notes on generalized gamma, beta and hypergeometric functions, J. Comput. Anal. Appl., 15 (2013), 1194-1201
##[2]
M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler's beta function, J. Comput. Appl. Math., 78 (1997), 19-23
##[3]
M. A. Chaudhry, A. Qadir, H. M. Srivastava, R. B. Paris, Extended hypergeometric and con uent hypergeometric functions, Appl. Math. Comput., 159 (2004), 589-602
##[4]
J. Choi, A. Hasanov, H. M. Srivastava, M. Turaev, Integral representations for Srivastava's triple hypergeometric functions, Taiwanese J. Math., 15 (2011), 2751-2762
##[5]
J. Choi, A. Hasanov, M. Turaev, Integral representations for Srivastava's hypergeometric function \(H_A\), Honam Math. J., 34 (2012), 113-124
##[6]
J. Choi, A. Hasanov, M. Turaev, Integral representations for Srivastava's hypergeometric function \(H_B\), J. Korean Soc. Math. Educ. Ser. B, Pure Appl. Math., 19 (2012), 137-145
##[7]
J. Choi, A. Hasanov, M. Turaev, Integral representations for Srivastava's hypergeometric function \(H_C\), Honam Math. J., 34 (2012), 473-482
##[8]
A. Hasanov, H. M. Srivastava, M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl., 324 (2006), 955-969
##[9]
M. J. Luo, G. V. Milovanovic, P. Agarwal, Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput., 248 (2014), 631-651
##[10]
M. J. Luo, R. K. Raina, Extended generalized hypergeometric functions and their applications, Bull. Math. Anal. Appl., 5 (2013), 65-77
##[11]
M. A. Özarslan, Some remarks on extended hypergeometric, extended con uent hypergeometric and extended Appell's functions, J. Comput. Anal. Appl., 14 (2012), 1148-1153
##[12]
M. A. Özarslan, E. Özergin, Some generating relations for extended hypergeometric functions via generalized fractional derivative operator, Math. Comput. Modelling, 52 (2010), 1825-1833
##[13]
E. Özergin, M. A. Özarslan, A. Altın, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math., 235 (2011), 4601-4610
##[14]
E. D. Rainville, Special functions, Reprint of 1960 first edition, Chelsea Publishing Co., Bronx, New York (1971)
##[15]
H. M. Srivastava, Hypergeometric functions of three variables, Ganita, 15 (1964), 97-108
##[16]
H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo, 16 (1967), 99-115
##[17]
H. M. Srivastava, P. Agarwal, S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput., 247 (2014), 348-352
##[18]
H. M. Srivastava, P. W. Karlsson, Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley and Sons, Inc.], New York (1985)
##[19]
H. M. Srivastava, R. K. Parmar, P. Chopra, A class of extended fractional derivative operators and associated generating relations involving hypergeometric functions,, Axioms, 1 (2012), 238-258
]
A novel approach of variable order derivative Theory and Methods
A novel approach of variable order derivative Theory and Methods
en
en
In order to solve problems posed while using the concept of fractional variable order derivative, we
introduce in this work a novel fractional variable order derivative. Our derivative has no singular kernel, this
allows it to well-describe the effect of memory. We present the relationship between the new derivative with
the well-known integral transforms. We present exact solution of some basic associated differential equations.
We presented the numerical approximation of the derivative for first and second order approximation.
4867
4876
Badr Saad T.
Alkahtani
Department of mathematics, colle of science
King Saud University
Saudi Arabia
balqahtani1@ksu.edu.sa
Ilknur
Koca
Department of Mathematics, Faculty of Sciences
Mehmet Akif Ersoy University
Turkey
ikoca@mehmetakif.edu.tr
Abdon
Atangana
Institute for groundwater Studies, Faculty of Natural and Agricultural Sciences
University of the Free State
South Africa
abdonatangana@yahoo.fr
New fractional variable order derivative
properties
numerical method.
Article.122.pdf
[
[1]
M. A. Abdelkawy, M. A. Zaky, A. H. Bhrawy, D. Baleanu, Numerical simulation of time variable fractional order mobile-immobile advection-dispersion model, Romanian Rep. Phys., 67 (2015), 773-791
##[2]
A. Atangana, A. Kilicman, On the Generalized Mass Transport Equation to the Concept of Variable Fractional Derivative, Math. Probl. Eng., 2014 (2014), 1-9
##[3]
A. Atangana, S. C. Oukouomi Noutchie, Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer, Abstr. Appl. Anal., 2013 (2013), 1-8
##[4]
A. Atangana, A. Secer, A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions, Abstr. Appl. Anal., 2013 (2013), 1-8
##[5]
C. F. M. Coimbra, Mechanics with variable-order differential operators, Ann. Phys., 12 (2003), 692-703
##[6]
G. R. J. Cooper, D. R. Cowan, Filtering using variable order vertical derivatives, Comput. Geosci., 30 (2004), 455-459
##[7]
E. H. Doha, A. H. Bhrawy, D. Baleanu, S. S. Ezz-Eldien, The operational matrix formulation of the Jacobi tau approximation for space fractional diffusion equation, Adv. Difference Equ., 2014 (2014), 1-14
##[8]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam (2006)
##[9]
R. Lin, F. Liu, V. Anh, I. Turner, Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation, Appl. Math. Comput., 212 (2009), 435-445
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A computational method for converter analysis using point symmetries
A computational method for converter analysis using point symmetries
en
en
The one-parameter point transformation method is applied to clarify the use of symmetries to describe
the effects of additive uncertainties on the state-space solutions of an affine control system. The trajectory
of the solution in the presence of general, bounded uncertainties gives an idea of system robustness. The
boost converter is used for illustration. A specific symmetry is computed under uncertainties and its effects
on a possible solution are investigated. A comparison of the method with other state-space methods shows
that it is an excellent approach if developed further.
4877
4887
Richard O.
Ocaya
Department of Physics
University of the Free-State
South Africa
ocayaro@ufs.ac.za
Lie point symmetries
boost converter
robustness
state-space
infinitesimal generator.
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A homotopy algorithm for computing the fixed point of self-mapping with inequality and equality constraints
A homotopy algorithm for computing the fixed point of self-mapping with inequality and equality constraints
en
en
In this paper, to compute the fixed point of self-mapping on general non-convex sets, a modified constraint
shifting homotopy algorithm for perturbing simultaneously both equality constraints and inequality
constraints is proposed and the global convergence of the smooth homotopy pathways is proven under some
mild conditions. The advantage of the newly constructed homotopy is that the initial point needs to be only
in the shifted feasible set, not necessarily, an interior point in the original feasible set, and hence it is more
convenient to be implemented than the existing results. Some numerical examples are also given to show
its feasibility and effectiveness.
4888
4896
Zhichuan
Zhu
Faculty of Statistics
School of Mathematics and Statistics
Jilin University of Finance and Economics
Northeast Normal University
China
China
zhuzcnh@126.com
Yang
Li
School of Computer Science and Engineering
Changchun University of Technology
China
liyangyaya1979@sina.com
Yanchun
Xing
Faculty of Statistics
Jilin University of Finance and Economics
China
xingyanchun778@163.com
Xiaoyin
Wang
Department of Mathematics
Tianjin Polytechnic University
China
wxywxq@163.com
Homotopy method
general non-convex sets
self-mapping
fixed point.
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Block methods for a convex feasibility problem in a Banach space
Block methods for a convex feasibility problem in a Banach space
en
en
In this paper, a convex feasibility problem is investigated based on a block method. Strong convergence theorems for common solutions of equilibrium problems and generalized asymptotically quasi-\(\phi\)-
nonexpansive mappings are established in a strictly convex and uniformly smooth Banach space which also
has the Kadec-Klee property. The results obtained in this paper unify and improve many corresponding
results announced recently.
4897
4908
Mingliang
Zhang
School of Mathematics and Statistics
Henan University
China
hdzhangml@yeah.net
Ravi P.
Agarwal
Department of Mathematics
Texas A&M University
U. S. A.
Agarwal@tamuk.edu
Banach space
block method
equilibrium problem
convex feasibility problem
variational inequality.
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]
The threshold behavior and periodic solution of stochastic SIR epidemic model with saturated incidence
The threshold behavior and periodic solution of stochastic SIR epidemic model with saturated incidence
en
en
We investigate degenerate stochastic SIR epidemic model with saturated incidence. For the constant
coefficients case, we achieve a threshold which determines the extinction and persistence of the epidemic
by utilizing Markov semigroup theory. Furthermore, we conclude that environmental white noise plays a
positive effect in the control of infectious disease in some sense comparing to the corresponding deterministic
system. For the stochastic non-autonomous system, we prove the existence of periodic solution.
4909
4923
Zhongwei
Cao
Department of Applied Mathematics
Jilin University of Finance and Economics
China
15397191@qq.com
Wenjie
Cao
School of Mathematics and Statistics
Northeast Normal University
China
335694758@qq.com
Xiaojie
Xu
School of Science
China University of Petroleum (East China)
China
50764555@qq.com
Qixing
Han
School of Mathematics
Changchun Normal University
China
hanqixing123@163.com
Daqing
Jiang
School of Science
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
China University of Petroleum (East China)
King Abdulaziz University
China
Saudi Arabia
daqingjiang2010@hotmail.com
SIR epidemic model
Markov semigroups
asymptotic stability
threshold
periodic solution.
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]
Hybrid iterative algorithm for an infinite families of closed, uniformly asymptotic regular and uniformly Bregman totally quasi-D-asymptotically nonexpansive mappings in Banach spaces
Hybrid iterative algorithm for an infinite families of closed, uniformly asymptotic regular and uniformly Bregman totally quasi-D-asymptotically nonexpansive mappings in Banach spaces
en
en
A new hybrid Bregman projection method is considered for finding common solutions of the set of common fixed points of an infinite family of closed, uniformly asymptotic regular and uniformly Bregman totally
quasi-D-asymptotically nonexpansive mappings, the set of solutions to a variational inequality problem and
the set of common solutions to a system of generalized mixed equilibrium problems, strong convergence theorems of common elements are proved by using new analysis techniques and Bregman mappings in the setting
of uniformly smooth and 2-uniformly convex real Banach spaces. Our results improve and generalize many
important known recent results in the current literature, because Bregman projection mapping generalizes
the generalized projection mapping and the metric projection mapping.
4924
4948
Renxing
Ni
Department of Mathematics
Shaoxing University
China
nrx1964@163.com
Hybrid Bregman projection method
Bregman totally quasi-D-asymptotically nonexpansive mapping
variational inequality problem
generalized mixed equilibrium problem
uniformly smooth Banach space
invex set
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R. X. Ni, J. C. Yao, The modified Ishikawa iterative algorithm with errors for a countable family of Bregman totally quasi-D-asymptotically nonexpansive mappings in reflexive Banach spaces, Fixed Point Theory Appl., 2015 (2015), 1-24
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Fixed Point Results and its Applications to the Systems of Non-linear Integral and Differential Equations of Arbitrary Order
Fixed Point Results and its Applications to the Systems of Non-linear Integral and Differential Equations of Arbitrary Order
en
en
In this manuscript, common fixed point results for self-mappings satisfying generalized weak integral type
contraction in the setting of G-metric space are established. Using the derived results, some applications to
the systems of non-linear integral and fractional differential equations are also discussed.
4949
4962
Muhammad
Shoaib
Department of Mathematics
University of Malakand
Pakistan
shoaibkhanbs@gmail.com
Muhammad
Sarwar
Department of Mathematics
University of Malakand
Pakistan
sarwarswati@gmail.com
Kamal
Shah
Department of Mathematics
University of Malakand
Pakistan
kamalshah408@gmail.com
Poom
Kumam
KMUTT Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science
Department of Medical Research
King Mongkuts University of Technology Thonburi (KMUTT)
King Mongkuts University of Technology Thonburi (KMUTT)
China Medical University Hospital, China Medical University
Thailand
Thailand
Taiwan
poom.kumam@mail.kmutt.ac.th
G-metric space
integral type contraction
alternating distance function
integral equations
fractional differential equations.
Article.128.pdf
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