]>
2016
9
3
ISSN 2008-1898
692
Positive solutions of p-Laplacian fractional differential equations with integral boundary value conditions
Positive solutions of p-Laplacian fractional differential equations with integral boundary value conditions
en
en
In this work, we investigate the existence of solutions of p-Laplacian fractional differential equations with
integral boundary value conditions. Using the five functionals fixed point theorem, the existence of multiple
positive solutions is obtained for the boundary value problems. An example is also given to illustrate the
effectiveness of our main result.
717
726
Yunhong
Li
College of Sciences
Hebei University of Science and Technology
P. R. China
mathhong@126.com
Guogang
Li
College of Sciences
Hebei University of Science and Technology
P. R. China
lgg-2000@163.com
Multiple positive solutions
p-Laplacian
the five functionals fixed point theorem.
Article.1.pdf
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[1]
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]
Fixed and common fixed point results for cyclic mappings of \(\Omega\)-distance
Fixed and common fixed point results for cyclic mappings of \(\Omega\)-distance
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en
Jleli and Samet in [M. Jleli, B. Samet, Int. J. Anal., 2012 (2012), 7 pages] pointed out that some of fixed
point theorems in G-metric spaces can be derived from classical metric spaces. In this paper, we utilize the
concept of \(\Omega\)-distance in sense of Saadati et al. [R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades, Math.
Comput. Modeling, 52 (2010), 797-801] to introduce new fixed point and common fixed point results for
mappings of cyclic form, through the concept of G-metric space in sense of Mustafa and Sims [ Z. Mustafa,
B. Sims, J. Nonlinear Convex Anal., 7 (2006), 289-297]. We underline that the method of Jleli and Samet
cannot be applied to our results.
727
735
Wasfi
Shatanawi
Department of Mathematics, Faculty of Science
Hashemite University
Jordan
wshatanawi@yahoo.com
Anwar
Bataihah
Department of Mathematics, Faculty of Science
Irbid National University
Jordan
anwerbataihah@gmail.com
Ariana
Pitea
Department of Mathematics and Informatics
University Politehnica of Bucharest
Romania
arianapitea@yahoo.com
Nonlinear contraction
G-metric space
common fixed point
\(\Omega\)-distance.
Article.2.pdf
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R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades, Fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Modeling, 52 (2010), 797-801
##[20]
B. Samet, C. Vetro, F. Vetro, Remarks on G-metric spaces, Int. J. Anal., 2013 (2013), 1-6
##[21]
W. Shatanawi, S. Manro, Fixed point results for cyclic (\(\phi,\psi,A,B\))-contraction in partial metric spaces , Fixed Point Theory Appl., 2012 (2012), 1-13
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W. Shatanawi, A. Pitea , Omega-distance and coupled fixed point in G-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-15
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W. Shatanawi, A. Pitea , Fixed and coupled fixed point theorems of \(\Omega\)-distance for nonlinear contraction, Fixed Point Theory Appl., 2013 (2013), 1-16
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W. Shatanawi, M. Postolache, Some fixed point results for a G-weak contraction in G-metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-19
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W. Shatanawi, M. Postolache, Common fixed point results for mappings under nonlinear contraction of cyclic form in ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-13
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C. Vetro , Best proximity points: convergence and existence theorems for p-cyclic mappings, Nonlinear Anal., 73 (2010), 2283-2291
]
Asymptotic behavior and a posteriori error estimates in Sobolev space for the generalized overlapping domain decomposition method for evolutionary HJB equation with nonlinear source terms. Part 1
Asymptotic behavior and a posteriori error estimates in Sobolev space for the generalized overlapping domain decomposition method for evolutionary HJB equation with nonlinear source terms. Part 1
en
en
A posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet
boundary conditions on the boundaries for the discrete solutions on subdomains of evolutionary HJB equation
with nonlinear source terms are established using the semi-implicit time scheme combined with a FInite
element spatial approximation. Also the techniques of the residual a posteriori error analysis are used. Moreover,
using Benssoussan-Lions' algorithm, an asymptotic behavior in \(H^1_0\)-norm is deduced. Furthermore,
the results of some numerical experiments are presented to support the theory.
736
756
Salah
Boulaaras
Department Of Mathematics, College Of Sciences and Arts
Al-Qassim University
Kingdom Of Saudi Arabia
saleh_boulaares@yahoo.fr
A posteriori error estimates
GODDM
Dirichlet boundary conditions
algorithm
asymptotic behavior.
Article.3.pdf
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]
Monotone hybrid methods for a common solution problem in Hilbert spaces
Monotone hybrid methods for a common solution problem in Hilbert spaces
en
en
The purpose of this article is to investigate generalized mixed equilibrium problems and uniformly L-Lipschitz continuous asymptotically \(\kappa\)-strict pseudocontractions in the intermediate sense based on a monotone hybrid method. Strong convergence theorems of common solutions are established in the framework of
Hilbert spaces.
757
765
Dongfeng
Li
School of Information Engineering
North China University of Water Resources and Electric Power
China
sylidf@yeah.net
Juan
Zhao
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power University
China
zhaojuanyu@126.com
Asymptotically strict pseudocontraction
asymptotically nonexpansive mapping
generalized mixed equilibrium problem
solution
fixed point.
Article.4.pdf
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]
Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals
Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals
en
en
Some inequalities of Hermite-Hadamard type for MT-convex functions via classical integrals and Riemann-
Liouville fractional integrals are introduced, respectively, and applications for special means are given. Some
error estimates for the trapezoidal formula are also obtained.
766
777
Wenjun
Liu
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
China
wjliu@nuist.edu.cn
Wangshu
Wen
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
China
vekestom@gmail.com
Jaekeun
Park
Department of Mathematics
Hanseo University
Republic of Korea
jkpark@hanseo.ac.kr
MT-convex function
Hermite-Hadamard inequality
Hölder inequality
fractional integral
trapezoidal formula.
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]
Heisenberg type uncertainty principle for continuous shearlet transform
Heisenberg type uncertainty principle for continuous shearlet transform
en
en
We prove a Heisenberg type uncertainty principle for the continuous shearlet transform, and study two
generalizations of it. Our work extends the shearlet theory.
778
786
Yu
Su
School of Mathematical Sciences
Xing Jiang Normal University
China
yizai52@qq.com
Uncertainty principle
continuous shearlet transform
shearlet.
Article.6.pdf
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[1]
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Common fixed point results for multi-valued mappings with some examples
Common fixed point results for multi-valued mappings with some examples
en
en
In this paper, we define the concepts of the (CLR)-property and the (owc)-property for two single-valued
mappings and two multi-valued mappings in metric spaces and give some new common fixed point results
for these mappings. Also, we give some examples to illustrate the main results in this paper. Our main
results extend and improve some results given by some authors.
787
798
Afrah Ahmad Noan
Abdou
Department of Mathematics
King Abdulaziz University
Saudi Arabia
aabdou@kau.edu.sa
Weakly compatible mappings
fixed point
coincidence point
the (CLR)-property
the (owc)-property
the (CLRf )-property.
Article.7.pdf
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[1]
M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188
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M. Eshaghi Gordji, H. Baghani, H. Khodaei, M. Ramezani, A generalization of Nadler's fixed point theorem, J. Nonlinear Sci. Appl., 3 (2010), 148-151
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B. Fisher, A common fixed point theorem for four mappings on a compact metric space, Bull. Inst. Math. Acad. Sinica, 12 (1984), 249-252
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H. K. Pathak, R. P. Agarwal, Y. J. Cho, Coincidence and fixed points for multi-valued mappings and its application to nonconvex integral inclusions, J. Comput. Appl. Math., 283 (2015), 201-217
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A. Roldán, W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces using the \((CLR_g)\)-property, Fuzzy Sets and Systems, (In press), -
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K. P. R. Sastry, I. S. R. Krishna Murthy, Common fixed points of two partially commuting tangential selfmaps on a metric space, J. Math. Anal. Appl., 250 (2000), 731-734
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S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.), 32 (1982), 149-153
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W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), 1-14
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W. Sintunavarat, P. Kumam, Gregus-type common fixed point theorems for tangential multi-valued mappings of integral type in metric spaces, Internat. J. Math. Math. Sci., 2011 (2011), 1-12
##[36]
W. Sintunavarat, D. M. Lee, Y. J. Cho, Mizoguchi-Takahashi's type common fixed point theorems without T- weakly commuting condition and invariant approximations, Fixed Point Theory Appl., 2014 (2014), 1-10
##[37]
N. Wairojjana, W. Sintunavarat, P. Kumam, Common tripled fixed point theorems for W-compatible mappings along with the \(CLR_g\)-property in abstract metric spaces, J. Inequal. Appl., 2014 (2014), 1-17
]
Some topological properties of fuzzy cone metric spaces
Some topological properties of fuzzy cone metric spaces
en
en
We prove Baire's theorem for fuzzy cone metric spaces in the sense of Öner et al. [T. Öner, M. B. Kandemir,
B. Tanay, J. Nonlinear Sci. Appl., 8 (2015), 610-616]. A necessary and sufficient condition for a fuzzy cone
metric space to be precompact is given. We also show that every separable fuzzy cone metric space is
second countable and that a subspace of a separable fuzzy cone metric space is separable.
799
805
Tarkan
Öner
Department of Mathematics, Faculty of Sciences
Muğla Sıtkı Koçman University
Turkey
tarkanoner@mu.edu.tr
Fuzzy cone metric space
Baire's theorem
separable
second countable.
Article.8.pdf
[
[1]
T. Bag, Fuzzy cone metric spaces and fixed point theorems of contractive mappings, Ann. Fuzzy Math. Inform., 6 (2013), 657-668
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Z. Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl., 86 (1982), 74-95
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M. A. Erceg, Metric spaces in fuzzy set theory , J. Math. Anal. Appl., 69 (1979), 205-230
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A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399
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A. George, P. Veeramani , On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365-368
##[6]
V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems, 115 (2000), 485-489
##[7]
L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
##[8]
O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), 215-229
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O. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336-344
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T. Öner, M. B. Kandemir, B. Tanay , Fuzzy cone metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 610-616
##[11]
S. Rezapour, R. Hamlbarani , Some notes on the paper: ''Cone metric spaces and fixed point theorems of contractive mappings'', J. Math. Anal. Appl., 332 (2007), 1468-1476
##[12]
B. Schweizer, A. Sklar, Statistical metric spaces , Pacific J. Math., 10 (1960), 313-334
##[13]
L. A. Zadeh , Fuzzy sets, Information and Control, 8 (1965), 338-353
]
Common tripled fixed point theorem for W-compatible mappings in fuzzy metric spaces
Common tripled fixed point theorem for W-compatible mappings in fuzzy metric spaces
en
en
In this paper we present a common tripled fixed point theorem for W-compatible mappings under \(\phi\)-
contractive conditions in fuzzy metric spaces. The result generalizes, extends and improves several classical
and very recent related results in literature. For instance, we obtain an extension of Theorem 2.5 in [S.
Sedghi, I. Altun, N. Shobe, Nonlinear Anal., 72 (2010), 1298-1304], an refinement of Theorem 4.1 in [X.
Zhu, J. Xiao, Nonlinear Anal., 74 (2011), 5475-5479] and an improvement of Theorem 11 in [A. Roldán,
J. Martínez-Moreno, C. Roldán, Fixed Point Theory Appl., 2013 (2013), 13 pages]. Finally, an example is
given to illustrate the usability of our main result.
806
818
Jing-Feng
Tian
College of Science and Technology
North China Electric Power University
P. R. China
tianjfhxm_ncepu@163.com
Xi-Mei
Hu
China Mobile Group Hebei Co., Ltd.
P. R. China
huxm_bd@163.com
Hong-Shan
Zhao
School of Electrical and Electronic Engineering
North China Electric Power University
P. R. China
zhaohshcn@126.com
Common tripled fixed point
tripled fixed point
fuzzy metric space
Hadžić type t-norm.
Article.9.pdf
[
[1]
H. Aydi, M. Abbas, W. Sintunavarat, P. Kumam, Tripled fixed point of W-compatible mappings in abstract metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-20
##[2]
V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897
##[3]
M. Borcut, V. Berinde , Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput., 218 (2012), 5929-5936
##[4]
J. X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833-1843
##[5]
A. George, P. Veeramani, On some result in fuzzy metric space, Fuzzy Sets and Systems, 64 (1994), 395-399
##[6]
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389
##[7]
O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Space, Kluwer Academic Publishers, Dordrecht (2001)
##[8]
I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), 336-344
##[9]
D. Miheţ , Fixed point theorems in fuzzy metric spaces using property E.A., Nonlinear Anal., 73 (2010), 2184-2188
##[10]
S. Radenović, A note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces, Appl. Math. Comput., 236 (2014), 367-372
##[11]
J. Rodríguez López, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147 (2004), 273-283
##[12]
A. Roldán, J. Martínez-Moreno, C. Roldán , Tripled fixed point theorem in fuzzy metric spaces and applications, Fixed Point Theory Appl., 2013 (2013), 1-13
##[13]
B. Samet, C. Vetro, Coupled fixed point, f-invariant set and fixed point of N-order, Ann. Funct. Anal., 1 (2010), 46-56
##[14]
B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North-Holland Publishing Co., New York (1983)
##[15]
S. Sedghi, I. Altun, N. Shobe , Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Anal., 72 (2010), 1298-1304
##[16]
X. Zhu, J. Xiao, Note on ''Coupled fixed point theorems for contractions in fuzzy metric spaces'', Nonlinear Anal., 74 (2011), 5475-5479
]
Conjugacy between trapezoid maps
Conjugacy between trapezoid maps
en
en
Trapezoid maps are a kind of continuous and piecewise linear maps with a
at top. By the conjugacy
relationship, we present a complete classification for four families of trapezoid maps. Firstly, using an
extension method, we construct all homeomorphic solutions of conjugacy equation \(\varphi \circ f = g \circ \varphi\) for some
non-monotone continuous maps f and g. Secondly, using an iterative construction method and an extension
method, we construct respectively all topological conjugacies for four families of trapezoid maps. Finally,
all construction algorithms are implemented in MATLAB, and three examples are illustrated to construct
topological conjugacies and a topological semi-conjugacy.
819
826
Yong-Guo
Shi
Key Laboratory of Numerical Simulation of Sichuan Province, College of Mathematics and Information Science
Neijiang Normal University
P. R. China
scumat@163.com
Trapezoid map
topological conjugacy
topological classification
conjugacy equation.
Article.10.pdf
[
[1]
J. Banks, V. Dragan, A. Jones , Chaos: a mathematical introduction, Cambridge University Press, Cambridge (2003)
##[2]
L. Block, E. M. Coven , Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval, Trans. Amer. Math. Soc., 300 (1987), 297-306
##[3]
K. M. Brucks, M. Misiurewicz, C. Tresser, Monotonicity properties of the family of trapezoidal maps, Comm. Math. Phys., 137 (1991), 1-12
##[4]
P. R. Halmos , Lectures on Ergodic Theory , Chelsea Publishing Co., New York (1960)
##[5]
S. J. Kolodzieski , Delta-pseudo orbit shadowing in a family of trapezoidal maps, Ph.D. Thesis, Stevens Institute of Technology, ProQuest LLC, Ann Arbor, MI (1991)
##[6]
J. D. Louck, N. Metropolis, Symbolic dynamics of trapezoidal maps , D. Reidel Publishing Co., Dordrecht (1986)
##[7]
H. Segawa, H. Ishitani , On the existence of a conjugacy between weakly multimodal maps, Tokyo J. Math. , 21 (1998), 511-521
##[8]
B. Schweizer, A. Sklar, Continuous functions that conjugate trapezoid functions, Aequationes Math., 28 (1985), 300-304
##[9]
G. Zhang, Conjugacy and iterative roots of a class of piecewise expanding self-maps (I), (in Chinese), Chin. Ann. Math., 13 (1992), 33-40
]
Existence and uniqueness of mild and classical solutions to fractional order Hadamard-type Cauchy problem
Existence and uniqueness of mild and classical solutions to fractional order Hadamard-type Cauchy problem
en
en
We consider the existence and uniqueness of a mild and classical solution to impulsive nonlocal conditions
fractional-order Hadamard-type Cauchy problem. The results are obtained by means of fixed point methods. Finally, we illustrate our results by an example of fractional-order Hadamard-type Cauchy problem.
827
835
Qutaibeh
Katatbeh
Department of Mathematics and Statistics, Faculty of Science and Arts
Jordan University of Science and Technology
Jordan
qutaibeh@just.edu.jo
Ahmad
Al-Omari
Faculty of Sciences, Department of Mathematics
Al al-Bayt University
Jordan
omarimutah1@yahoo.com
Hadamard fractional derivative
integral boundary conditions
fixed point theorems
impulsive equations.
Article.11.pdf
[
[1]
B. Ahmad, S. K. Ntouyas, On Hadamard fractional integro-differential boundary value problems, J. Appl. Math. Comput., 47 (2015), 119-131
##[2]
B. Ahmad, S. K. Ntouyas, A. Alsaedi, New results for boundary value problems of Hadamard-type fractional differential inclusions and integral boundary conditions, Bound. Value Probl., 2013 (2013), 1-14
##[3]
A. Anguraja, M. L. Maheswari, Existence of solutions for fractional impulsive neutral functional infinite delay integrodifferential equations with nonlocal conditions, J. Nonlinear Sci. Appl., 5 (2012), 271-280
##[4]
P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl., 269 (2002), 387-400
##[5]
P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Fractional calculus in the Mellin setting and Hadamard-type fractional integrals, J. Math. Anal. Appl., 269 (2002), 1-27
##[6]
P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl., 270 (2002), 1-15
##[7]
J. Hadamard , Essai sur l'étude des fonctions donnés par leur développement de Taylor, J. Math. Pures Appl., 8 (1892), 101-186
##[8]
A. A. Kilbas , Hadamard-type fractional calculus, J. Korean Math. Soc., 38 (2001), 1191-1204
##[9]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V., Amsterdam (2006)
##[10]
A. A. Kilbas, J. J. Trujillo, Hadamard-type integrals as G-transforms, Integral Transforms Spec. Funct., 14 (2003), 413-427
##[11]
S.-Y. Lin, Generalized Gronwall inequalities and their applications to fractional differential equations, J. Inequal. Appl., 2013 (2013), 1-9
##[12]
J. A. Nanwarea, D. B. Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl., 7 (2014), 246-254
##[13]
T. Qiu, Z. Bai, Positive solutions for boundary of nonlinear fractional differential equation, J. Nonlinear Sci. Appl., 1 (2008), 123-131
]
Pedal curves of fronts in the sphere
Pedal curves of fronts in the sphere
en
en
Notions of the pedal curves of regular curves are classical topics. T. Nishimura [T. Nishimura, Demonstratio
Math., 43 (2010), 447-459] has done some work associated with the singularities of pedal curves of regular
curves. But if the curve has singular points, we can not define the Frenet frame at these singular points. We
also can not use the Frenet frame to define and study the pedal curve of the original curve. In this paper,
we consider the differential geometry of pedal curves of singular curves in the sphere. We define the pedal
curve of a front and give properties of such pedal curve by using a moving frame along a front. At last, we
give the classification of singularities of the pedal curves of fronts.
836
844
Yanlin
Li
School of Mathematics and Statistics
Northeast Normal University
P. R. China
liyl744@nenu.edu.cn
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Pedal curve
front
singularity
Legendre curve.
Article.12.pdf
[
[1]
V. I. Arnol'd , The geometry of spherical curves and the algebra of quaternions, Russian Math. Surveys, 50 (1995), 1-68
##[2]
T. Fukunaga, M. Takahashi , Existence and uniqueness for Legendre curves, J. Geom., 104 (2013), 297-307
##[3]
T. Fukunaga, M. Takahashi, Evolutes of fronts in the Euclidean plane, J. Singul., 10 (2014), 92-107
##[4]
T. Nishimura, Normal forms for singularities of pedal curves produced by non-singular dual curve germs in \(S^n\) , Geometriae Dedicata, 133 (2008), 59-66
##[5]
T. Nishimura, Singularities of pedal curves produced by singular dual curve germs in \(S^n\), Demonstratio Math., 43 (2010), 447-459
##[6]
M. Takahashi , Legendre curves in the unit spherical bundle and evolutes, , (Preprint), -
##[7]
C. T. C. Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc., 13 (1981), 481-539
]
Suzuki type theorems for asymmetric type mappings
Suzuki type theorems for asymmetric type mappings
en
en
We introduce a modified asymmetric \(G^\bigstar(\psi\varphi)\)-contractive mapping with respect to a general family of
functions \(G^*\) and establish asymmetric type fixed point results for such mappings. As an application of
our results, we deduce Suzuki type fixed point results via these mappings. We also derive certain fixed
point results for asymmetric type mappings in partial G-metric spaces. Moreover, we discuss an illustrative
example to highlight the realized improvements.
845
859
M.
Paknazar
Department of Mathematics
Farhangian University
Iran.
m.paknazar@cfu.ac.ir
M. A.
Kutbi
Department of Mathematics
King Abdulaziz University
Saudi Arabia
mkutbi@yahoo.com
M.
Demma
Università degli Studi di Palermo
Italy
martanoir91@hotmail.it
P.
Salimi
Young Researchers and Elite Club
Islamic Azad University--Rasht Branch
Iran
salimipeyman@gmail.com
G-metric space
partial G-metric space
fixed point
Suzuki fixed point theorem.
Article.13.pdf
[
[1]
M. Abbas, T. Nazir, P. Vetro, Common fixed point results for three maps in G-metric spaces, Filomat, 25 (2011), 1-17
##[2]
H. Aydi, W. Shatanawi, C. Vetro , On generalized weak G-contraction mapping in G-metric spaces, Comput. Math. Appl., 62 (2011), 4223-4229
##[3]
F. Moradlou, P. Salimi, P. Vetro, Some new extensions of Edelstein-Suzuki-type fixed point theorem to G-metric and G-cone metric spaces, Acta Math. Sci. Ser. B Engl. Ed., 33 (2013), 1049-1058
##[4]
Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory, PhD Thesis, the University of Newcastle, Australia (2005)
##[5]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297
##[6]
R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades, Fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Modelling, 52 (2010), 797-801
##[7]
P. Salimi, P. Vetro, A result of Suzuki type in partial G-metric spaces, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 274-284
##[8]
B. Samet, C. Vetro, F. Vetro, From metric spaces to partial metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-11
##[9]
C. Vetro, F. Vetro, Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results , Topology Appl., 164 (2014), 125-137
]
Bernoulli polynomials of the second kind and their identities arising from umbral calculus
Bernoulli polynomials of the second kind and their identities arising from umbral calculus
en
en
In this paper, we study the Bernoulli polynomials of the second kind with umbral calculus viewpoint and
derive various identities involving those polynomials by using umbral calculus.
860
869
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
S. Korea
tkkim@kw.ac.kr; kimtk2015@gmail.com
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Dmitry V.
Dolgy
School of Natural Sciences
Far Eastern Federal University
Russia
d_dol@mail.ru
Jong-Jin
Seo
Department of Applied Mathematics
Pukyong National University
S. Korea
seo2011@pknu.ac.kr
Bernoulli polynomial of the second kind
umbral calculus.
Article.14.pdf
[
[1]
A. Bayad, T. Kim, Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials, Russ. J. Math. Phys., 18 (2011), 133-143
##[2]
A. Bottreau, A. Di Bucchianico, D. E. Loeb, Computer algebra and umbral calculus, Proceedings of the 7th conference on formal power series and algebraic combinatorics, Discrete Math., 180 (1998), 65-72
##[3]
D. Ding, J. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math., 20 (2010), 7-21
##[4]
S. B. Ekhad, D. Zeilberger, Using Rota's umbral calculus to enumerate Stanley's P-partitions, Adv. in Appl. Math., 41 (2008), 206-213
##[5]
T. Ernst, Examples of a q-umbral calculus, Adv. Stud. Contemp. Math., 16 (2008), 1-22
##[6]
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Lagrangians of the \((2+ 1)\)-dimensional KP equation with variable coefficients and cross terms
Lagrangians of the \((2+ 1)\)-dimensional KP equation with variable coefficients and cross terms
en
en
Zhang constructed a Lagrangian for the (2 + 1)-dimensional KP equation with variable coefficients and
cross terms [L. H. Zhang, Appl. Math. Comput., 219 (2013), 4865-4879]. This paper suggests a simple
method to construct a needed Lagrangian using the semi-inverse by introducing a simple auxiliary function,
the presented method is simpler than Zhang's method to construct a Lagrangian.
870
872
Hong-Yan
Liu
School of Fashion Technology
National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering
Zhongyuan University of Technology
Soochow University
China
China
phdliuhongyan@yahoo.com
Ji-Huan
He
National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering
Soochow University
China
hejihuan@suda.edu.cn
Zhi-Min
Li
Rieter (China) Textile Instrument Co.
China
Variational principle
least square technology
semi-inverse method.
Article.15.pdf
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[1]
S. Das, R. Kumar, Fractional diffusion equations in the presence of reaction terms, J. Comput. Complex. Appl., 1 (2015), 15-21
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D. D. Fei, F. J. Liu, P. Wang, H. Y. Liu, , A short remark on He-Lee's variational principle for heat conduction, Therm. Sci., 17 (2013), 1561-1563
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J. H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fractals, 19 (2004), 847-851
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J. H. He, Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern Phys. B, 20 (2006), 1141-1199
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J. H. He, An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Internat. J. Modern Phys. B, 22 (2008), 3487-3578
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J. H. He, Asymptotic methods for solitary solutions and compactons, Abstr. Appl. Anal., 2012 (2012), 1-130
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Z. Jia, M. Hu, Q. Chen, Variational principle for unsteady heat conduction equation, Therm. Sci., 18 (2014), 1045-1047
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X. W. Li, Y. Li, J. H. He, On the semi-inverse method and variational principle, Therm. Sci., 17 (2013), 1565-1568
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Z. B. Li, J. Liu, Variational formulations for soliton equations arising in water transport in porous soils, Therm. Sci., 17 (2013), 1483-1485
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G. Wu, D. Baleanu, Z. Deng, Variational iteration method as a kernel constructive technique, Appl. Math Model., 39 (2015), 4378-384
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L. H. Zhang, Conservation Laws of the (2 + 1)-dimensional KP equation and Burgers equation with variable coefficients and cross terms, Appl. Math. Comput., 219 (2013), 4865-4879
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X. W. Zhou, L.Wang, A variational principle for coupled nonlinear Schrodinger equations with variable coefficients and high nonlinearity, Comput. Math. Appl., 61 (2011), 2035-2038
]
Ran-Reurings fixed point theorem is an immediate consequence of the Banach contraction principle
Ran-Reurings fixed point theorem is an immediate consequence of the Banach contraction principle
en
en
In this short note, we prove in few lines that Ran-Reurings fixed point theorem [A. C. M. Ran, M. C. B.
Reurings, Proc. Amer. Math. Soc., 132 (2004), 1435-1443] is an immediate consequence of the famous
Banach contraction principle.
873
875
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Fixed point
Ran-Reurings fixed point theorem
Banach contraction principle.
Article.16.pdf
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[1]
S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fundam. Math., 3 (1922), 133-181
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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
]
Hermite--Hadamard type integral inequalities via (s,m)--P--convexity on co-ordinates
Hermite--Hadamard type integral inequalities via (s,m)--P--convexity on co-ordinates
en
en
In this paper, the notion of (s;m)-P-convex functions on the co-ordinates is introduced and several integral inequalities of the Hermite-Hadamard type for co-ordinated (s;m)-P-convex functions are established.
876
884
Ying
Wu
College of Mathematics
Inner Mongolia University for Nationalities
China
wuying19800920@qq.com
Feng
Qi
Department of Mathematics, College of Science
Tianjin Polytechnic University
China
qifeng618@gmail.com; qifeng618@hotmail.com
Zhi-Li
Pei
College of Computer Science and Technology
Inner Mongolia University for Nationalities
China
zhilipei@sina.com
Shu-Ping
Bai
College of Mathematics
Inner Mongolia University for Nationalities
China
bsp0838@126.com
Co-ordinates
(s،m)-P-convex function
Hermite-Hadamard's integral inequality
integral identity.
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]
A fixed point theorem on soft G-metric spaces
A fixed point theorem on soft G-metric spaces
en
en
We introduce soft G-metric spaces via soft element. Then, we obtain soft convergence and soft continuity
by using soft G-metric. Also, we prove a fixed point theorem for mappings satisfying sufficient conditions
in soft G-metric spaces.
885
894
Aysegul Caksu
Guler
Faculty of Science, Department of Mathematics
Ege University
Turkey
aysegul.caksu.guler@ege.edu.tr
Esra Dalan
Yildirim
Faculty of Science and Letters, Department of Mathematics
Yaşar University
Turkey
esra.dalan@yasar.edu.tr
Oya Bedre
Ozbakir
Faculty of Science, Department of Mathematics
Ege University
Turkey
oya.ozbakir@ege.edu.tr
Soft set
soft metric space
generalized metric space
soft G-metric space
fixed point.
Article.18.pdf
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[1]
M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On Some New Operations In Soft Set Theory , Comput. Math. Appl., 57 (2003), 1547-1553
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Z. Mustafa, H. Obeidat, F. Awawdeh, Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces, Fixed Point Theory Appl., 2008 (2008), 1-12
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Z. Mustafa, W. Shatanawi, M. Batanieh, Existence of Fixed Point Results in G-Metric Spaces, Int. J. Math. Math. Sci., 2009 (2009), 1-10
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H. K. Nashine, Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., 5 (2012), 1-13
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M. Shabir, M. Naz, On Soft Topological Spaces, Comput. Math. Appl., 61 (2011), 1786-1799
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Q. Tu, C. Zhu, Z. Wu, Common fixed point theorems under strict contractive conditions in Menger probabilistic G-metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 1176-1189
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D. Wardowski , On A Soft Mapping And Its Fixed Points, Fixed Point Theory Appl., 2013 (2013), 1-11
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I. Zorlutuna, M. Akda~g, W. K. Min, S. Atmaca, Remarks On Soft Topological Spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171-185
]
Banach fixed point theorem from the viewpoint of digital topology
Banach fixed point theorem from the viewpoint of digital topology
en
en
The present paper studies the Banach contraction principle for digital metric spaces such as digital
intervals, simple closed k-curves, simple closed 18-surfaces and so forth. Furthermore, we prove that a
digital metric space is complete, which can strongly contribute to the study of Banach fixed point theorem
for digital metric spaces. Although Ege, et al. [O. Ege, I. Karaca, J. Nonlinear Sci. Appl., 8 (2015),
237-245] studied \Banach fixed point theorem for digital images", the present paper makes many notions
and assertions of the above mentioned paper refined and improved.
895
905
Sang-Eon
Han
Department of Mathematics Education, Institute of Pure and Applied Mathematics
Chonbuk National University
Republic of Korea
sehan@jbnu.ac.kr
Banach fixed point theorem
digital contraction map
Banach contraction principle
digital image
digital continuity
digital topology.
Article.19.pdf
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S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., 3 (1922), 133-181
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O. Ege, I. Karaca , Banach fixed point theorem for digital images, J. Nonlinear. Sci. Appl., 8 (2015), 237-245
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S. E. Han, Non-product property of the digital fundamental group, Inform. Sci., 171 (2005), 73-91
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S. E. Han, On the simplicial complex stemmed from a digital graph, Honam Math. J., 27 (2005), 115-129
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S. E. Han, Connected sum of digital closed surfaces, Inform. Sci., 176 (2006), 332-348
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S. E. Han, Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces, Inform. Sci., 176 (2006), 120-134
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S. E. Han, Continuities and homeomorphisms in computer topology and their applications, J. Korean Math. Soc., 45 (2008), 923-952
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S. E. Han, Equivalent \((k_0; k_1)\)-covering and generalized digital lifting, Inform. Sci., 178 (2008), 550-561
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S. E. Han, The k-homotopic thinning and a torus-like digital image in \(Z^n\) , J. Math. Imaging. Vision., 31 (2008), 1-16
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S. E. Han, Digital version of the fixed point theory, Proceedings of 11th ICFPTA (Abstracts) , (2015)
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S. E. Han, Remarks on the Lefschetz fixed point theorem for digital images, , (submitted), -
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S. E. Han, B. G. Park, Digital graph \((k_0; k_1)\)-isomorphism and its applications, atlas-conference, (2003)
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S. Jain, S. Jain, L. B. Jain, On Banach contraction principle in a cone metric space, J. Nonlinear Sci. Appl., 5 (2012), 252-258
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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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]
On the multilevel nonlinear problem and its convergence algorithms
On the multilevel nonlinear problem and its convergence algorithms
en
en
In this paper, applying the geometrical knowledge of Hilbert spaces, we investigate and analyze a system
of multilevel split fixed point problems (MSFP). New split solution algorithms are introduced and strong
convergence theorems for (MSFP) are established. At the end of this paper, as an application of our results,
we investigate and analyze a system of multilevel split variational inclusion problems (MSVIP) and some
strong convergence solution for (MSVIP) are obtained. These results obtained by this paper improve and
develop some known ones in the literature.
906
919
Zhenhua
He
Department of Mathematics
Department of Mathematics
Tongji University
Honghe University
P. R. China
China
zhenhuahe@126.com
Jitao
Sun
Department of Mathematics
Honghe University
China
sunjt@sh163.net
Multilevel nonlinear problem
nonexpansive mapping
variational inclusion problem
split solution algorithm
strong convergence theorem.
Article.20.pdf
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L. C. Ceng, Q. H. Ansari, J. C. Yao, Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem, Nonlinear Anal., 75 (2012), 2116-2125
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Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
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Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587-600
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S. S. Chang, L. Wang , Strong convergence theorems for the general split variational inclusion problem in Hilbert spaces, Fixed Point Theory Appl., 2014 (2014), 1-14
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C. E. Chidume, N. Shahzad , Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal., 62 (2005), 1149-1156
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Z. He, The split equilibrium problems and its convergence algorithms, J. Inequal. Appl., 2012 (2012), 1-15
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Z. He, W. S. Du, New feasible iterative algorithms and strong convergence theorems for bilevel split equilibrium problems, Fixed Point Theory Appl., 2014 (2014), 1-17
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W. Takahashi , Nonlinear Functional Analysis, Fixed Point Theory and Its Applications, Yokohama Publishers, Yokohama, Japan (2000)
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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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X. Yu, N. Shahzad, Y. Yao, Implicit and explicit algorithms for solving the split feasibility problem , Optim. lett., 6 (2012), 1447-1462
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J. Zhao, S. He, Strong convergence of the viscosity approximation process for the split common fixed-point problem of quasi-nonexpansive mapping, J. Appl. Math., 2012 (2012), 1-12
]
Common fixed point theorems for compatible and weakly compatible maps in Menger probabilistic G-metric spaces
Common fixed point theorems for compatible and weakly compatible maps in Menger probabilistic G-metric spaces
en
en
In this paper, we prove some new common fixed point theorems for compatible and weakly compatible
self-maps under \(\phi\)-contractive conditions in Menger probabilistic G-metric spaces. Our results improve and
generalize many comparable results in existing literature. Finally, an example is given as an application of
our main results.
920
932
Xiaohuan
Mu
Department of Mathematics
Nanchang University
P. R. China
xiaohuanmu@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
wuzhaoqi_conquer@163.com
Menger probabilistic G-metric space
common fixed point
compatible maps
weakly compatible maps.
Article.21.pdf
[
[1]
R. P. Agarwal, Z. Kadelburg, S. Radenović , On coupled fixed point results in asymmetric G-metric spaces , J. Inequal. Appl., 2013 (2013), 1-12
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R. P. Agarwal, E. Karapınar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed point theory Appl., 2013 (2013), 1-33
##[3]
J. X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833-1843
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J. X. Fang, Y. Gang, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal., 70 (2009), 184-193
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]
Fixed points and dynamics on generating function of Genocchi numbers
Fixed points and dynamics on generating function of Genocchi numbers
en
en
Recently, there have been many works related with dynamics of various functions. In this paper, singular
values and fixed points of generating function of Genocchi numbers, \(g_\lambda(z) = \lambda \frac{2z}
{e^z+1}, (\lambda\in R) > 1\), are
investigated. It is shown that the function \(g_\lambda(z)\) has infinitely many singular values and its critical values
lie in the left half plane and one point on the real axis in the right half plane. Further, the real fixed
points of \(g_\lambda(z)\) and their nature are determined. Finally, we provide numerical evidence of the existence of
chaotic phenomena by illustrating bifurcation diagrams of system and by calculating the Lyapunov exponent.
933
939
Dongkyu
Lim
Department of Mathematics
Kyungpook National University
S. Korea
dgrim84@gmail.com
Fixed point
Genocchi number
chaos.
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M. Sajid, Singular values and fixed points of family of generating function of Bernoulli's numbers , J. Nonlinear Sci. Appl., 8 (2015), 17-22
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M. Sajid, A. S. Alsuwaiyan, Chaotic behavior in the real dynamics of a one parameter family of functions, Int. J. Appl. Sci. Eng., 12 (2014), 289-301
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]
Random coupled and tripled best proximity results with cyclic contraction in metric spaces
Random coupled and tripled best proximity results with cyclic contraction in metric spaces
en
en
We consider random best proximity point and cyclic contraction pair problems in uniformly convex
Banach spaces. We also prove some tripled best proximity and tripled fixed point theorems in complete
metric spaces. Our results present random version of [W. Sintunavarat, P. Kumam, Fixed point Theory
Appl., 2012 (2012), 16 pages] and many others.
940
956
Farhana
Akbar
Department of Mathematics
GDCW
Pakistan
ridaf75@yahoo.com
Marwan Amin
Kutbi
Department of Mathematics
King Abdulaziz University
Saudi Arabia
mkutbi@ yahoo.com
Masood Hussain
Shah
Department of Mathematics, SBSSE
Lahore University of Management Sciences
Pakistan
mshah@lums.edu.pk
Naeem
Shafqat
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauudin Zakariya University
Pakistan
naeem781625@yahoo.com
Partially ordered set
coupled best proximity point
tripled best proximity point
random best proximity point.
Article.23.pdf
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[1]
M. Abbas, N. Hussain, B. E. Rhoades, Coincidence point theorems for multivalued f-weak contraction mappings and applications, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 105 (2011), 261-272
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R. P. Agarwal, D. O. Regan, M. Sambandham, Random and deterministic fixed point theory for generalized contractive maps, Appl. Anal., 83 (2004), 711-725
##[3]
S. S. Basha, Best proximity point theorems generalizing the contraction principal, Nonlinear Anal., 74 (2011), 5844-5850
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S. S. Basha, P. Veeramani , Best proximity pairs and best approximations, Acta Sci. Math. (Szeged), 63 (1997), 289-300
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S. S. Basha, P. Veeramani, Best proximity pair theorems for multifunctions with open fibers, J. Approx. Theory, 103 (2000), 119-129
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S. S. Basha, P. Veeramani, D. V. Pai , Best proximity pair theorems, Indian J. Pure Appl. Math., 32 (2001), 1237-1246
##[7]
I. Beg, A. R. Khan, N. Hussain, Approximation of \(\star\)-nonexpansive random multivalued operators on Banach spaces, J. Australian . Math. Soc., 76 (2004), 51-66
##[8]
L. Ćirić, J. S. Ume, S. N. Ješić, On random coincidence for a pair of measurable mappings, Ital. J. Pure Appl. Math., 23 (2008), 37-44
##[9]
L. Ćirić, V. Lakshmikantham, Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces , Stoch. Anal. Appl., 27 (2009), 1246-1259
##[10]
A. A. Eldred, P. Veeramani , Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006
##[11]
K. Fan, Extensions of two fixed point theorems of F. E. , Browder, Math. Z., 112 (1969), 234-240
##[12]
N. J. Huang, Aprinciple of randomization of coincidence points with appliactions, Appl. Math. Lett., 12 (1999), 107-113
##[13]
N. Hussain , Asymptotically pseudo-contractions, Banach operator pairs and best simultaneous approximations, Fixed Point Theory Appl., 2011 (2011), 1-11
##[14]
N. Hussain, M. abbas, A. Azam, J. Ahmad, Coupled coincidence point results for a generalized compatible pair with applications, Fixed Point Theory Appl., 2014 (2014), 1-20
##[15]
N. Hussain, V. Berinde, N. Shafqat, Common fixed point and approximation results for generalized \(\phi\)-contractions, Fixed Point Theory, 10 (2009), 111-124
##[16]
N. Hussain, A. Latif, N. Shafqat, Weak contractive inequalities and compatible mixed monotone random operators in ordered metric spaces, J. Inequal. Appl., 2012 (2012), 1-20
##[17]
S. Ioth, A random fixed point theorem for a multi-valued contraction mapping, Pac. J. Math., 68 (1977), 85-90
##[18]
A. R. Khan, N. Hussain, Random coincidence point theoremin Frechet spaces with applications, Stochastic Anal. Appl., 22 (2004), 155-167
##[19]
A. R. Khan, N. Hussain, N. Yasmin, N. Shafqat, Random coincidence point results for weakly increasing functions in partially ordered metric spaces, Bull. Iranian Math. Soc., 41 (2015), 407-422
##[20]
M. A. Kutbi, J. Ahmad, M. Abbas, M. Arshad, Trippled coincidence and common fixed results for two pairs of hybrid mappings , Abstract Appl. Anal., 2014 (2014), 1-11
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T. C. Lin, Random approximations and random fixed point theorems for non-self-maps, Proc. Amer. Math. Soc., 103 (1988), 1129-1135
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C. Mongkolkeha, P. Kumam, Best proximity point theorems for generalized cyclic contractions in ordered metric spaces, J. Optim. Theory Appl., 155 (2012), 215-226
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W. Sintunavarat, P. Kumam, Coupled best proximity point theorem in metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-16
##[30]
T. Suzuki, M. Kikkawa, C. Vetro , The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., 71 (2009), 2918-2926
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D. H. Wagner, Survey of measurable selection theorems, SIAM J. Control Optim., 15 (1977), 859-903
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K. Wlodarczyk, R. Plebaniak, A. Banach, Best proximity points for cyclic and noncyclic set-valued relatively quas-asymptotic contractions in uniform spaces, Nonlinear Anal., 70 (2009), 3332-3342
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X. H. Zhu, J. Z. Xiao, Random periodic point and fixed point results for random monotone mappings in ordered Polish spaces, Fixed Point Theory Appl., 2010 (2010), 1-13
]
Monotone projection algorithms for various nonlinear problems in Hilbert spaces
Monotone projection algorithms for various nonlinear problems in Hilbert spaces
en
en
In this paper, a monotone projection algorithm is investigated for solving common solutions of a fixed
point problem of an asymptotically strict pseudocontraction, an equilibrium problem and a zero problem of
the sum of two monotone mappings. Strong convergence theorems are established in the framework of real
Hilbert spaces.
957
966
B. A. Bin
Dehaish
Department of mathematics, Faculty of Science
AL Faisaliah Campus, King Abdulaziz University
Saudi Arabia
bbendehaish@kau.edu.sa
H. O.
Bakodah
Department of mathematics, Faculty of Science
AL Faisaliah Campus, King Abdulaziz University
Saudi Arabia
hbakodah@kau.edu.sa
A.
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
X.
Qin
Department of Mathematics
Department of Mathematics
Wuhan University of Technology
King Abdulaziz University
China
Saudi Arabia
ljjhqxl@aliyun.com
Hilbert space
equilibrium problem
variational inequality
nonexpansive mapping
fixed point.
Article.24.pdf
[
[1]
A. S. Antipin, Solution methods for variational inequalities with coupled constraints, Comput. Math. Math. Phys., 40 (2000), 1239-1254
##[2]
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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P. Cheng, H. Wu, On asymptotically strict pseudocontractions and equilibrium problems, J. Inequal. Appl., 2013 (2013), 1-16
##[7]
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
##[8]
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
##[9]
W. Cholamjiak, P. Cholamjiak, S. Suantai, Convergence of iterative schemes for solving fixed point problems for multi-valued nonself mappings and equilibrium problems, J. Nonlinear Sci. Appl., 8 (2015), 1245-1256
##[10]
B. S. Choudhury, S. Kundu, A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem, J. Nonlinear Sci. Appl., 5 (2012), 243-251
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K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174
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R. H. He, Coincidence theorem and existence theorems of solutions for a system of Ky Fan type minimax inequalities in FC-spaces, Adv. Fixed Point Theory, 2 (2012), 47-57
##[13]
C. Huang, X. Ma, On generalized equilibrium problems and strictly pseudocontractive mappings in Hilbert spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
##[14]
S. M. Kang, S. Y. Cho, Z. Liu, Convergence of iterative sequences for generalized equilibrium problems involving inverse-strongly monotone mappings, J. Inequal. Appl., 2010 (2010), 1-16
##[15]
J. K. Kim, Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-\(\phi\)-nonexpansive mappings , Fixed Point Theory Appl., 2011 (2011), 1-15
##[16]
J. K. Kim, P. N. Anh, Y. M. Nam, Strong convergence of an extended extragradient method for equilibrium problems and fixed point problems, J. Korean Math. Soc., 49 (2012), 187-200
##[17]
M. Liu, S. S. Chang , An iterative method for equilibrium problems and quasi-variational inclusion problems, Nonlinear Funct. Anal. Appl., 14 (2009), 619-638
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P. E. Mainge, A hybird extragradient-viscosity method for monotone operators and fixed point problems , SIAM J. Control Optim., 47 (2008), 1499-1515
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S. Park , Applications of the KKM principle on abstract convex minimal spaces, Nonlinear Funct. Anal. Appl., 13 (2008), 179-191
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L. Qihou, Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings, Nonlinear Anal., 26 (1996), 1835-1845
##[21]
X. Qin, S. Y. Cho, L.Wang, A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-10
##[22]
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
##[23]
Y. Qing, S. Lv , A strong convergence theorem for solutions of equilibrium problems and asymptotically quasi-\(\phi\)- nonexpansive mappings in the intermediate sense, Fixed Point Theory Appl., 2013 (2013), 1-14
##[24]
R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 149 (1970), 75-88
##[25]
D. R. Sahu, H. K. Xu, J. C. Yao, Asymptotically strict pseudocontractive mappings in the intermediate sense, Nonlinear Anal., 70 (2009), 3502-3511
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J. Shen, L. P. Pang, An approximate bundle method for solving variational inequalities, Commun. Optim. Theory, 1 (2012), 1-18
##[27]
T. V. Su, Second-order optimality conditions for vector equilibrium problems, J. Nonlinear Funct. Anal., 2015 (2015), 1-31
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L. Sun, Hybrid methods for common solutions in Hilbert spaces with applications, J. Inequal. Appl., 2014 (2014), 1-16
##[29]
A. Tada, W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem, J. Optim. Theory Appl., 133 (2007), 359-370
##[30]
J. Zhao, Strong convergence theorems for equilibrium problems, fixed point problems of asymptotically nonexpansive mappings and a general system of variational inequalities, Nonlinear Funct. Appl. Appl., 16 (2011), 447-464
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L. C. Zhao, S. S. Chang, Strong convergence theorems for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Nonlinear Sci. Appl., 2 (2009), 78-91
]
Polynomiography via an iterative method corresponding to Simpsons \(\frac{1}{3}\) rule
Polynomiography via an iterative method corresponding to Simpsons \(\frac{1}{3}\) rule
en
en
The aim of this paper is to present some artwork produced via polynomiography of a few complex
polynomials and a few special polynomials arising in science as well as a few considered to arrive at beautiful
but anticipated designs. In this paper an iterative method corresponding to Simpson's \(\frac{1}{3}\) rule is used instead
of Newton's method. The word ''polynomiography'' coined by Kalantari for that visualization process. The
images obtained are called polynomiographs. Polynomiographs have importance for both the art and science
aspects. By using an iterative method corresponding to Simpson's \(\frac{1}{3}\) rule, we obtain quite new nicely looking
polynomiographs that are different from Newton's method. Presented examples show that we obtain very
interesting patterns for complex polynomial equations, permutation matrices, doubly stochastic matrices,
Chebyshev polynomial, polynomial arising in physics and Alexander polynomial in knot theory. We believe
that the results of this paper enrich the functionality of the existing polynomiography software.
967
976
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Shahid M.
Ramay
College of Science, Physics and Astronomy Department
King Saud University
Saudi Arabia
schaudhry@ksu.edu.sa
Muhmmad
Tanveer
Department of Mathematics and Statistics
University of Lahore
Pakistan
tanveer.7955180@yahoo.com
Waqas
Nazeer
Division of Science and Technology
University of Education
Pakistan
nazeer.waqas@ue.edu.pk
Polynomiography
Newton's method
Simpson's \(\frac{1}{3}\) rule.
Article.25.pdf
[
[1]
R. M. Ashish, R. Chugh, Julia sets and Mandelbrot sets in Noor orbit , Appl. Math. Comput., 228 (2014), 615-631
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A. Cayley , The Newton-Fourier imaginary problem, Amer. J. Math., 2 (1879), 97-97
##[3]
K. Gdawiec, W. Kotarski, A. Lisowska, Polynomiography based on the nonstandard Newton-like root finding methods, Abstr. Appl. Anal., 2015 (2015), 1-19
##[4]
G. Julia , Mémoire sur literation des fonctions rationnelles, J. Math. Pures Appl., 8 (1918), 47-246
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B. Kalantari , Method of creating graphical works based on polynomials, Patent, US6894705 (2005)
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B. Kalantari , Polynomiography: From the Fundamental Theorem of Algebra to Art , Leonardo, 38 (2005), 233-238
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B. Kalantari , Polynomial Root-finding and Polynomiography , World Scientific Publishing Co. Pte. Ltd., New Jersey (2009)
##[8]
B. Kalantari, Alternating sign matrices and polynomiography, Electron. J. Combin., 2011 (2011), 1-22
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S. M. Kang, H. H. Alsulami, A. Rafiq, A. A. Shahidd , S-iteration scheme and polynomiography, J. Nonlinear Sci. Appl., 8 (2015), 617-627
##[10]
W. Kotarski, K. Gdawiec, A. Lisowska, Polynomiography via Ishikawa and Mann iterations , Adv. Visual Comput., 7431 (2012), 305-313
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H. Minc, Nonnegative Matrices, John Wiley & Sons, New York (1988)
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B. Prasad, B. Katiyar, Fractals via Ishikawa iteration , Control, Comput. Inform. Systems, 140 (2011), 197-203
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M. Rani, R. Chugh , Dynamics of antifractals in Noor orbit, Inter. J. Comput. Appl., 57 (2012), 11-15
##[15]
S. L. Singh, S. Jain, S. N. Mishra , A new approach to superfractals, Chaos, Solitons Fractals, 42 (2009), 3110-3120
##[16]
H. Susanto, N. Karjanto , Newtons methods basins of attraction revisited, Appl. Math. Comput., 215 (2009), 1084-1090
]
Random quadruple coincidence points theorems for sequence of random mappings and application
Random quadruple coincidence points theorems for sequence of random mappings and application
en
en
In this paper, we give the definitions of compatibility and weakly reciprocally continuity for sequence of
random mappings \(T_i\) and a random self-mapping g. Further, using these definitions we establish quadruple
random coincidence and quadruple random fixed point results by applying the concept of an \(\alpha\)-series for
sequence of mappings, introduced by Sihag et al. [V. Sihag, R. K. Vats, C. Vetro, Quaest. Math., 37 (2014),
1-6], in the setting of partially ordered metric spaces. Our results are some random versions and extensions
of results relating to triple fixed points theorems by R. K. Vats et al. [R. K. Vats, K. Tas, V. Sihag, A.
Kumar, J. Inequal. Appl., 2014 (2014), 12 pages], we also give some examples to illustrate our results.
977
988
Xiaofang
Yan
Department of Mathematics
Nanchang University
P. R. China
xiaoxiaoyan_green@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
wuzhaoqi_conquer@163.com
Random quadruple coincidence point
quadruple random fixed point
\(\alpha\)-series
partially ordered metric space.
Article.26.pdf
[
[1]
A. Alotaibi, S. Alsulami , Coupled coincidence points for monotone operators in partially ordered metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-13
##[2]
V. Berinde, M. Borcut , Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897
##[3]
T. G. Bhaskar, V. Lakshmikantham , Fixed point theorems in partially ordered metric spaces and applications , Nonlinear Anal., 65 (2006), 1379-1393
##[4]
L. Ćirić, V. Lakshmikantham, Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stoch. Anal. Appl., 27 (2009), 1246-1259
##[5]
C. J. Himmelberg, Measurable relations, Fund. Math., 87 (1975), 53-72
##[6]
N. Hussain, A. R. Khan, R. P. Agarwal , Krasnosel'skii and Ky Fan type fixed point theorems in ordered Banach spaces, J. Nonlinear Convex Anal., 11 (2010), 475-489
##[7]
N. Hussain, A. Latif, N. Shafqat, Weak contractive inequalities and compatible mixed monotone random operators in ordered metric spaces, J. Inequal. Appl., 2012 (2012), 1-20
##[8]
S. Itoh, A random fixed point theorem for a multi-valued contraction mapping, Pac. J. Math., 68 (1977), 85-90
##[9]
B. Jiang, S. Xu, L. Shi , Coupled coincidence points for mixed monotone random operators in partially ordered metric spaces, Abstr. Appl. Anal., 2014 (2014), 1-9
##[10]
E. Karapinar, N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Comput. Math. Appl., 64 (2012), 1839-1848
##[11]
A. Khan, N. Hussain, Random coincidence point theorem in Frechet spaces with applications, Stochastic Anal. Appl., 22 (2004), 155-167
##[12]
V. Lakshmikantham, L.Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
##[13]
G. Z. Li, H. Duan, On Random Fixed Point Theorems of Random Monotone Operators, Appl. Math. Lett., 18 (2005), 1019-1026
##[14]
S. Li, X. Xiao, L. Li, J. Lv, Random Approximation with Weak Contraction Random Operators and a Random Fixed Point Theorem for Nonexpansive Random Self-mappings, J. Inequal. Appl., 2012 (2012), 1-7
##[15]
T. C. Lin, Random approximations and random fixed point theorems for non-self maps, Proc. Amer. Math. Soc., 103 (1988), 1129-1135
##[16]
E. J. McShane, R. B. J. Warified , On Filippov's implicit functions lemma, Proc. Amer. Math. Soc., 18 (1967), 41-47
##[17]
Z. Mustafa, H. Aydi, E. Karapinar , Mixed g-monotone property and quadruple fied point theorems in partially ordered metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-19
##[18]
H. K. Nashine, B. Samet, Fixed Point Results for Mappings Satisfying ( \(\psi,\varphi\))-weakly Contractive Condition in Partially Ordered Metric Spaces, Nonlinear Anal., 74 (2010), 2201-2209
##[19]
R. T. Rockafellar , Measurable dependence of convex sets and functions in parameters, J. Math. Anal. Appl., 28 (1969), 4-25
##[20]
M. Saha, N. Ganguly , Random Fixed Point Theorem on a Ćirić-type Contractive Mapping and Its Consequence, Fixed Point Theory Appl., 2012 (2012), 1-18
##[21]
V. Sihag, R. K. Vats, C. Vetro, A fixed point theorem in G-metric spaces via \(\alpha\)-series, Quaest. Math., 37 (2014), 1-6
##[22]
R. K. Vats, K. Tas, V. Sihag, A. Kumar, Triple Fixed Point Theorems Via \(\alpha\)-series in Partially Ordered Metric Spaces, J. Inequal. Appl., 2014 (2014), 1-12
##[23]
D. H. Wagner , Survey of measurable selection theorems , SIAM J. Control Optim., 15 (1977), 859-903
##[24]
C. Zhu, C. Chen , Calculations of random fixed point index, J. Math. Anal. Appl., 339 (2008), 839-844
##[25]
C. Zhu, Z. Xu, Random Ambiguous Point of Random \(K(\omega)\)-set-contractive Operator, J. Math. Anal. Appl., 328 (2006), 2-6
##[26]
X. H. Zhu, J. Z. Xiao, Random Periodic Point and Fixed Point Results for Random Monotone Mappings in Ordered Polish Spaces, Fixed Point Theory Appl., 2010 (2010), 1-13
]
The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities
The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities
en
en
In this paper, we introduce several stronger forms of sensitivities in the dynamical systems of semigroup
actions, such as thick sensitivity and thickly syndetical sensitivity, and obtain some sufficient conditions for
a dynamical system to have such sensitivities. We prove that a weakly mixing system of semigroup actions
is thickly sensitive and a minimal weakly mixing system as well as a nonminimal M-system of semigroup
actions is thickly syndetically sensitive.
989
997
Tao
Wang
Department of Mathematics
Nanchang University
P. R. China
taowangmath@163.com
Jiandong
Yin
Department of Mathematics
Nanchang University
P. R. China
axf@163.com
Qi
Yan
Department of Mathematics
Nanchang University
P. R. China
qiyanmath@163.com
Semigroup action
thick sensitivity
thickly syndetical sensitivity
weakly mixing.
Article.27.pdf
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[1]
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H. Y. Wang, G. F. Zhu, Y. Tang, L. Huang, Some dynamical properties of syndetic subsemigroups actions, J. Dyn. Control. Syst., 21 (2015), 147-154
]
A new Householders method free from second derivatives for solving nonlinear equations and polynomiography
A new Householders method free from second derivatives for solving nonlinear equations and polynomiography
en
en
In this paper, we describe the new Husehölder's method free from second derivatives for solving nonlinear
equations. The new Husehölder's method has convergence of order five and efficiency index \(5^{\frac{1}{3}} \approx 1.70998\),
which converges faster than the Newton's method, the Halley's method and the Husehölder's method.
The comparison table demonstrate the faster convergence of our method. Polynomiography via the new
Husehölder's method is also presented.
998
1007
Waqas
Nazeer
Division of Science and Technology
University of Education
Pakistan
nazeer.waqas@ue.edu.pk
Muhmmad
Tanveer
Department of Mathematics and Statistics
University of Lahore
Pakistan
tanveer.7955180@yahoo.com
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Amir
Naseem
Department of Mathematics
Lahore Leads University
Pakistan
amir14514573@yahoo.com
Nonlinear equation
Newton's method
Halley's method
Husehölder's method
polynomiography.
Article.28.pdf
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[1]
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]
On the evolution differential inclusions under a noncompact evolution system
On the evolution differential inclusions under a noncompact evolution system
en
en
We study the existence of mild solutions to differential inclusions with nonlocal conditions. The first
result is established when evolution system is equicontinuous and multifunction is upper semi-continuous.
Then another result is obtained when evolution system is not equicontinuous and not compact. The measure
of noncompactness and the fixed point theorem for multivalued mappings play key roles in the proof. An
example is provided to illustrate our results.
1008
1018
Min
Wang
Library
Huaiyin Institute of Technology
P. R. China
wmmath@163.com
Shaochun
Ji
Faculty of Mathematics and Physics
Huaiyin Institute of Technology
P. R. China
jiscmath@163.com
Shu
Wen
Faculty of Mathematics and Physics
Huaiyin Institute of Technology
P. R. China
wenshu@hyit.edu.cn
nonlocal conditions
measure of noncompactness
Differential inclusions
fixed point theorems
mild solutions.
Article.29.pdf
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[1]
R. P. Agarwal, M. Meehan, D. O'Regan , Fixed Point Theory and Aplications, Cambridge University Press, Cambridge (2001)
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R. P. Agarwal, J. Banas, B. C. Dhage, S. D. Sarkate, Attractivity results for a nonlinear functional integral equation, Georgian Math. J., 18 (2011), 1-19
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I. Benedetti, N. V. Loi, L. Malaguti , Nonlocal problems for differential inclusions in Hilbert Spaces, Set-Valued Var. Anal., 22 (2014), 639-656
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]
Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales
Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales
en
en
In this paper, we first propose a single-species system with impulsive effects on time scales and by
establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain
sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem
for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the
existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system.
Finally, we give an example to show the feasibility of our main results. Our example also shows that the
continuous time system and its corresponding discrete time system have the same dynamics. Our results of
this paper are completely new.
1019
1034
Yongkun
Li
Department of Mathematics
Yunnan University, Kunming
People's Republic of China
yklie@ynu.edu.cn
Pan
Wang
Department of Mathematics
Yunnan University, Kunming
People's Republic of China
wp521009@126.com
Bing
Li
Department of Mathematics
Yunnan University, Kunming
People's Republic of China
bli123@126.com
Impulsive single-species model
comparison theorem
permanence
almost periodic solution
time scales.
Article.30.pdf
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[1]
R. P. Agarwal, M. Bohner, T. Li, C. Zhang, Oscillation criteria for second-order dynamic equations on time scales, Appl. Math. Lett., 31 (2014), 34-40
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M. Bohner, A. Peterson , Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston (2001)
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M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston (2003)
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L. Bourdin, E. Trélat , General Cauchy-Lipschitz theory for \(\Delta\)-Cauchy problems with Caratheodory dynamics on time scales, J. Difference Equ. Appl., 20 (2014), 526-547
##[5]
M. G. Huang, W. Z. Feng, Oscillation criteria for impulsive dynamic equations on time scales, J. Differential Equations, 2007 (2007), 1-9
##[6]
Y. K. Li, C. Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr. Appl. Anal., 2011 (2011), 1-22
##[7]
Y. K. Li, L. Yang, H. T. Zhang , Permanence and uniformly asymptotical stability of almost periodic solutions for a single-species model with feedback control on time scales, Asian-Eur. J. Math., 2014 (2014), 1-15
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K. R. Prasad, R. A. Kameswara, B. Bharathi , Positive solutions for system of 2n-th order Sturm-Liouville boundary value problems on time scales, Proc. Indian Acad. Sci. Math. Sci., 124 (2014), 67-79
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Y. Su, Z. Feng, Homoclinic orbits and periodic solutions for a class of Hamiltonian systems on time scales , J. Math. Anal. Appl., 411 (2014), 37-62
##[13]
R. H. Tan, Z. X. Li, S. L. Guo, Z. J. Liu, Analysis of a periodic single species population model involving constant impulsive perturbation, J. Appl. Math., 2014 (2014), 1-7
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R. H. Tan, Z. J. Liu, R. A. Cheke, Periodicity and stability in a single-species model governed by impulsive differential equation, Appl. Math. Model., 36 (2012), 1085-1094
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##[16]
Y. H. Zhi, Z. L. Ding, Y. K. Li, Permanence and almost periodic solution for an enterprise cluster model based on ecology theory with feedback controls on time scales, Discrete Dyn. Nat. Soc., 2013 (2013), 1-14
##[17]
J. W. Zhou, Y. K. Li, Sobolev's spaces on time scales and its applications to a class of second order Hamiltonian systems on time scales, Nonlinear Anal., 73 (2010), 1375-1388
]
Iterative methods for solving scalar equations
Iterative methods for solving scalar equations
en
en
In this paper, we establish new iterative methods for the solution of scalar equations by using the
decomposition technique mainly due to Daftardar-Gejji and Jafari [V. Daftardar-Gejji, H. Jafari, J. Math.
Anal. Appl., 316 (2006), 753-763].
1035
1042
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Faisal
Ali
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Pakistan
faisalali@bzu.edu.pk
Arif
Rafiq
Department of Mathematics and Statistics
Virtual University of Pakistan
Pakistan
aarafiq@gmail.com
Iterative methods
nonlinear equations
order of convergence
multiple roots
Article.31.pdf
[
[1]
S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations modified Adomian decomposition method, Appl. Math. Comput., 145 (2003), 887-893
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G. Adomian, Nonlinear Stochastic Systems and Applications to Physics, Kluwer Academic Publishers, Dordrecht (1989)
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E. Babolian, J. Biazar, On the order of convergence of Adomian method, Appl. Math. Comput., 130 (2002), 383-387
##[4]
E. Babolian, J. Biazar, Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput., 132 (2002), 167-172
##[5]
C. Chun, Iterative methods improving Newton's method by the decomposition method, Comput. Math. Appl., 50 (2005), 1559-1568
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C. Chun, H. J. Bae, B. Neta, New families of nonlinear third-order solvers for finding multiple roots, Comput. Math. Appl., 57 (2009), 1574-1582
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C. Chun, Y. Ham, A one-parameter fourth-order family of iterative methods for nonlinear equations, Appl. Math. Comput., 189 (2007), 610-614
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C. Chun, B. Neta, A third-order modification of Newton's method for multiple roots, Appl. Math. Comput., 211 (2009), 474-479
##[9]
C. Chun, B. Neta, Basin of attraction for Zhou-Chen-Song fourth order family of methods for multiple roots, Math. Comput. Simulation, 109 (2015), 74-91
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V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl., 316 (2006), 753-763
##[11]
V. I. Hasanov, I. G. Ivanov, G. Nedzhibov, A new modification of Newton's method, Appl. Math. Engin. Econom. (Sozopol, 2001), pp. 278-286, Heron Press, Sofia (2002)
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H. H. H. Homeier, On Newton-type methods for multiple roots with cubic convergence , J. Comput. Appl. Math., 231 (2009), 249-254
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E. Isaacson, H. B. Keller, Analysis of Numerical Methods, John Wiley & Sons, Inc., New York (1966)
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B. Neta, C. Chun , On a family of Laguerre methods to find multiple roots of nonlinear equations, Appl. Math. Comput., 219 (2013), 10987-11004
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B. Neta, C. Chun, M. Scott, On a development of iterative methods for multiple roots, Appl. Math. Comput., 244 (2013), 358-361
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N. Osada, An optimal multiple root-finding method of order three, J. Comput. Appl. Math., 51 (1994), 131-133
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E. Schröder, Über unendlich viele algorithmen zur auflösung der gleichungen, Math. Ann., 2 (1870), 317-365
]
Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property
Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property
en
en
By means of weakening conditions of the gauge function \(\phi\) and the CLRg property, some common fixed
point theorems are established in fuzzy metric spaces. The two mappings considered here are assumed
to be weakly compatible. Our results extend and improve very recent theorems in the related literature.
1043
1051
Shuang
Wang
School of Mathematical Sciences
Yancheng Teachers University, Yancheng
P. R. China
wangshuang19841119@yahoo.com
Fuzzy metric spaces
weakly compatible mappings
common fixed points
common limit in the range property.
Article.32.pdf
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[1]
M. Aamri, D. E. Moutawakil , Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188
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M. Abbas, M. A. Khan, S. Radenovic , Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202
##[3]
L. Ćirić , Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces, Non-linear Anal., 72 (2010), 2009-2018
##[4]
J. X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833-1843
##[5]
J. X. Fang, On \(\varphi\)-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets and Systems, 267 (2015), 86-99
##[6]
A. Francisco, R. L. Hierroa, W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces using the CLRg property, Fuzzy Sets and Systems, 282 (2014), 131-142
##[7]
A. George, P. Veeramani, On some result in fuzzy metric space, Fuzzy Sets and Systems, 64 (1994), 395-399
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T. Gnana-Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
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M. Grabiec, Fixed points in fuzzy metric spaces , Fuzzy Sets and Systems, 27 (1988), 385-389
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V. Gregori, S. Morillas, A. Sapena, On a class of completable fuzzy metric spaces, Fuzzy Sets and Systems, 161 (2010), 2193-2205
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O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht (2001)
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X. Q. Hu, Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-14
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X. Q. Hu, M. Xue Zheng, B. Damjanović, X. F. Shao, Common coupled fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-11
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M. Jain, K. Tas, S. Kumar, N. Gupta, Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg property in fuzzy metric spaces, J. Appl. Math., 2012 (2012), 1-13
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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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D. O'Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput., 195 (2008), 86-93
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K. P. R. Sastry, I. S. R. Krishna Murthy, Common fixed points of two partially commuting tangential selfmaps on a metric space, J. Math. Anal. Appl., 250 (2000), 731-734
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W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), 1-14
]
The Dynamics and Solution of some Difference Equations
The Dynamics and Solution of some Difference Equations
en
en
In this paper, we study solution and periodic nature of the following difference equations
\[x_{n+1} =\frac{
x_{n-1}x_{n-5}}{
x_{n-3}(\pm 1 \pm x_{n-1}x_{n-5})}
;\quad n = 0; 1; ...;\]
where the initial conditions \(x_{-5}; x_{-4}; x_{-3}; x_{-2}; x_{-1}; x_0\) are arbitrary positive real numbers. we studied the
equilibrium points of the given equation. Some qualitative properties such as the global stability, and the
periodic character of the solutions in each case have been studied. We presented some numerical examples
by using random initial values and the coefficients of each case. Some figures have been given to explain
the behavior of the obtained solutions by using MATLAB to confirm the obtained results.
1052
1063
A.
Khaliq
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
khaliqsyed@gmail.com
E. M.
Elsayed
Department of Mathematics, Faculty of Science
Mathematics Department, Faculty of Science
Mansoura University
King Abdulaziz University
Egypt
Saudi Arabia
emmelsayed@yahoo.com
Periodicity
stability
rational difference equations.
Article.33.pdf
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[1]
R. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker Inc., New York (1992)
##[2]
M. Aloqeili , Dynamics of a rational difference equation, Appl. Math. Comput., 176 (2006), 768-774
##[3]
M. B. Bekker, M. J. Bohner, H. D. Voulov, Asymptotic behavior of solutions of a rational system of difference equations, J. Nonlinear Sci. Appl., 7 (2014), 379-382
##[4]
C. Cinar, On the positive solutions of the difference equation \(x_{n+1 }=\frac{ ax_{n-1}}{ 1+bx_nx_{n-1}} \), Appl. Math. Comp., 156 (2004), 587-590
##[5]
H. Chen, H. Wang, Global attractivity of the difference equation \(x_{n+1} =\frac{ x_n + \alpha x_{n-1} }{\beta + x_n}\), Appl. Math. Comput., 181 (2006), 1431-1438
##[6]
Q. Din, E. M. Elsayed, Stability analysis of a discrete ecological model, Comput. Ecol. Softw., 4 (2014), 89-103
##[7]
E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, On the difference equations \(x_{n+1} =\frac{ \alpha x_{n-k}}{ \beta + \gamma\Pi ^k_{ i=0} x_{n-i}}\), J. Concr. Appl. Math., 5 (2007), 101-113
##[8]
E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, Qualitative behavior of higher order difference equation, Soochow J. Math., 33 (2007), 861-873
##[9]
E. M. Elsayed, Qualitative behaviour of difference equation of order two, Math. Comput. Modelling, 50 (2009), 1130-1141
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E. M. Elsayed, Solution and attractivity for a rational recursive sequence, Discrete Dyn. Nat. Soc., 2011 (2011), 1-17
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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
##[12]
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, New method to obtain periodic solutions of period two and three of a rational difference equation, Nonlinear Dynam., 79 (2015), 241-250
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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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T. F. Ibrahim, On the third order rational difference equation \(x_{n+1} = \frac{x_nx_{n-2}}{ x_{n-1}(a + bx_nx_{n-2})}\), Int. J. Contemp. Math. Sci., 4 (2009), 1321-1334
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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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V. L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht (1993)
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M. R. S. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall, CRC Press, London (2001)
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A. S. Kurbanli, On the behavior of solutions of the system of rational difference equations, World Appl. Sci. J., 10 (2010), 1344-1350
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H. Ma, H. Feng, J. Wang, W. Ding, Boundedness and asymptotic behavior of positive solutions for dierence equations of exponential form, J. Nonlinear Sci. Appl., 8 (2015), 893-899
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Full state hybrid projective synchronization of variable-order fractional chaotichyperchaotic systems with nonlinear external disturbances and unknown parameters
Full state hybrid projective synchronization of variable-order fractional chaotichyperchaotic systems with nonlinear external disturbances and unknown parameters
en
en
The full state hybrid projective synchronization (FSHPS) definition for variable-order fractional
chaotic/hyperchaotic systems with nonlinear external disturbances and unknown parameters is firstly presented.
Then by introducing a compensator and a nonlinear controller, the FSHPS scheme is generated to
eliminate the in
uence of nonlinear external disturbances effectively. Moreover, the parameters are estimated
validly. Based on these control methods, appropriate parameters and controller to achieve FSHPS for the
variable-order fractional chaotic/hyperchaotic systems are chosen impactfully. Simulations of variable-order
fractional Chen and Lü system and fractional order hyperchaotic Lorenz system in the sense of FSHPS are
performed and results show the effectiveness of our method.
1064
1076
Li
Zhang
College of Control Science and Engineering
Business School
Shandong University
Shandong University of Political Science and Law
China
China
zhanglisdu2008@yahoo.com
Tao
Liu
Business School
Shandong University of Political Science and Law
China
pkutaotao@163.com
Variable-order fractional systems
synchronization
external disturbance
unknown parameters
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]
Some Identities of q-Euler Polynomials under the Symmetric Group of Degree n
Some Identities of q-Euler Polynomials under the Symmetric Group of Degree n
en
en
In this paper, we investigate some new symmetric identities for the q-Euler polynomials under the
symmetric group of degree n which are derived from fermionic p-adic q-integrals on \(\mathbb{Z}_p\).
1077
1082
T.
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
S. Korea
tkkim@kw.ac.kr
D. S.
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
H.-I.
Kwon
Department of Mathematics
Kwangwoon University
S. Korea
sura@kw.ac.kr
J.-J.
Seo
Department of Applied Mathematics
Pukyong National University
S. Korea
seo2011@pknu.ac.kr
D. V.
Dolgy
Hanrimwon
Kwangwoon University
Republic of Korea
d_dol@mail.ru
Identities of symmetry
Carlitz-type q-Euler polynomial
symmetric group of degree n
fermionic p-adic q-integral.
Article.35.pdf
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[1]
A. Bayad, T. Kim, Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials, Russ. J. Math. Phys., 18 (2011), 133-143
##[2]
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##[8]
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]
Generalized mixed equilibrium and fixed point problems in a Banach space
Generalized mixed equilibrium and fixed point problems in a Banach space
en
en
In this paper, a quasi-\(\phi\)-nonexpansive mapping and a generalized mixed equilibrium problem are in-
vestigated. A strong convergence theorem of common solutions is established in a non-uniformly convex
Banach space. The results presented in the paper improve and extend some recent results.
1083
1092
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
Korea
ooly61@hotmail.com
Algorithm
equilibrium problem
quasi-\(\phi\)-nonexpansive mapping
nonexpansive mapping
fixed point.
Article.36.pdf
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]
A further generalization of certain integral inequalities similar to Hardys inequality
A further generalization of certain integral inequalities similar to Hardys inequality
en
en
In this paper, we investigate certain integral inequalities similar to Hardy's inequality. By introducing
a monotonous function, we establish generalized versions of some known results related to the Hardy's
inequality and give some new integral inequalities of Hardy-type.
1093
1102
Shanhe
Wu
Department of Mathematics
Longyan University
P. R. China
shanhewu@gmail.com
Banyat
Sroysang
Department of Mathematics and Statistics
Thammasat University
Thailand
b.sroysang@gmail.com
Shuguang
Li
Department of Mathematics
Longyan University
P. R. China
shuguanglily@sina.com
Hardy's inequality
Hölder's inequality
similar version
generalization
integral inequalities.
Article.37.pdf
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[1]
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]
A new general algorithm for set-valued mappings and equilibrium problem
A new general algorithm for set-valued mappings and equilibrium problem
en
en
We consider a multi-step algorithm to approximate a common element of the set of solutions of monotone
and Lipschitz-type continuous equilibrium problems, and the set of common fixed points of a finite family
of set-valued mappings satisfying condition (E). We prove strong convergence theorems of such an iterative
scheme in real Hilbert spaces. This common solution is the unique solution of a variational inequality
problem and it satisfies the optimality condition for a minimization problem. The main result extends
various results exiting in the literature.
1103
1115
Javad
Vahidi
Department of Mathematics
Iran University of Science and Technology
Iran
jvahidi@iust.ac.ir
Equilibrium problem
variational inequality
set-valued mapping
condition (E).
Article.38.pdf
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[1]
A. Abkar, M. Eslamian, Convergence theorems for a finite family of generalized nonexpansive multivalued mappings in CAT(0) spaces, Nonlinear Anal., 75 (2012), 1895-1903
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A. Abkar, M. Eslamian , Geodesic metric spaces and generalized nonexpansive multivalued mappings, Bull. Iranian Math. Soc., 39 (2013), 993-1008
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P. N. Anh, Strong convergence theorems for nonexpansive mappings and Ky Fan inequalities, J. Optim. Theory Appl., 154 (2012), 303-320
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P. N. Anh, A hybrid extragradient method extended to fixed point problems and equilibrium problems, Optimization, 62 (2013), 271-283
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P. N. Anh, J. K. Kim, L. D. Muu, An extragradient algorithm for solving bilevel pseudomonotone variational inequalities, J. Global Optim., 52 (2012), 627-639
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Some new coupled fixed point theorems in partially ordered complete probabilistic metric spaces
Some new coupled fixed point theorems in partially ordered complete probabilistic metric spaces
en
en
In this paper, we weaken the notion of \(\Psi\) of Luong and Thuan, [V. N. Luong, N. X. Thuan, Nonlinear
Anal., 74 (2011), 983-992] and prove some new coupled coincidences and coupled common fixed point
theorems for mappings having a mixed g-monotone property in partially ordered complete probabilistic
metric spaces. As an application, we discuss the existence and uniqueness for a solution of a nonlinear
integral equation.
1116
1128
Qiang
Tu
Department of Mathematics
Nanchang University
P. R. China
qiangtu126@126.com
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
Zhaoqi
Wu
Department of Mathematics
Nanchang University
P. R. China
wuzhaoqi_conquer@163.com
Xiaohuan
Mu
Department of Mathematics
Nanchang University
P. R. China
xiaohuanmu@163.com
Coupled fixed point
mixed g-monotone mappings
partially ordered
probabilistic metric space.
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Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings
Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings
en
en
In this paper, we present some fixed point theorems for cyclic admissible generalized contractions involving C-class functions and admissible mappings in metric-like spaces. We obtain some new results which
extend and improve many recent results in the literature. In order to illustrate the effectiveness of the
obtained results, several examples and applications to functional equations arising in dynamic programming
are also given.
1129
1142
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Huseyin
Isik
Department of Mathematics, Faculty of Science
Department of Mathematics
University of Gazi
Mus Alparslan University
Turkey
Turkey
isikhuseyin76@gmail.com
Arslan H.
Ansari
Department of Mathematics
Karaj Branch, Islamic Azad University
Iran
amiranalsismath3@gmail.com
Common fixed point
C-class functions
admissible mappings
partial metric space
metric-like space.
Article.40.pdf
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]
\(L_p\)-dual mixed geominimal surface areas
\(L_p\)-dual mixed geominimal surface areas
en
en
Zhu, Zhou and Xu showed an integral formula of \(L_p\)-mixed geominimal surface area by the p-Petty body.
In this paper, we give an integral representation of \(L_p\)-dual mixed geominimal surface area and establish
several related inequalities.
1143
1152
Yan
Li
Department of Mathematics
China Three Gorges University
P. R. China
Wang
Weidong
Department of Mathematics
China Three Gorges University
P. R. China
wangwd722@163.com
Si
Lin
Department of Mathematics
Beijing Forestry University
P. R. China
\(L_p\)-mixed geominimal surface area
\(L_p\)-dual mixed geominimal surface area
integral representation.
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Y. B. Feng, W. D. Wang , \(L_p\)-dual geominimal surface area, Glasgow. Math. J., 56 (2014), 229-239
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Y. N. Li, W. D. Wang, The \(L_p\)-dual mixed geominimal surface area for multiple star bodies, J. Inequal. Appl., 2014 (2014), 1-10
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D. P. Ye, On the \(L_p\) geominimal surface area and related inequalities, arXiv, (submitted), 1-1308
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C. Zhu, J. Z. Zhou, W. X. Xu, Affine isoperimetric inequalities for \(L_p\) geominimal surface area, Springer Proc. Math. Stat., 106 (2014), 167-176
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]
A new branch and bound algorithm for integer quadratic programming problems
A new branch and bound algorithm for integer quadratic programming problems
en
en
For integer quadratic programming problems, a new branch and bound algorithm is proposed in this
paper through a series of improvements on the traditional branch and bound algorithm, which can be
used to solve integer quadratic programming problems effectively and efficiently. This algorithm employs
a new linear relaxation and bound method and a rectangular deep bisection method. At the same time, a
rectangular reduction strategy is used to improve the approximation degree and speed up the convergence
of the algorithm. Numerical results show that the proposed algorithm is feasible and effective and has
improved the existing relevant branch and bound algorithms.
1153
1164
Xiaohua
Ma
Institute of Information and System Sciences
Beifang University for Nationalities
China
mxh6464@163.com
Yuelin
Gao
Institute of Information and System Sciences
Beifang University for Nationalities
China
gaoyuelin@263.net
Xia
Liu
Institute of Information and System Sciences
Beifang University for Nationalities
China
liuxia_929@163.com
Integer quadratic programming
branch and bound
linear relaxation
rectangular deep bisection
rectangular reduction.
Article.42.pdf
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C. Buchheim, L. Trieu, Quadratic outer approximation for convex integer programming with box constraints, Exp. Algorithms, 7933 (2013), 224-235
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Z. P. Chen, F. Xi , A new branch-and-bound algorithm for solving large complex integer convex quadratic programs, Math. Numer. Sin., 26 (2004), 445-458
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Y. L. Gao, F. Wei, A branch-and-bound reduced method for a class of non-negative integer quadratic programming problems, math. Numer. sin., 33 (2011), 233-248
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]
Fixed point theorems for generalized (\(\alpha_*-\psi\))-Ćirić-type contractive multivalued operators in b-metric spaces
Fixed point theorems for generalized (\(\alpha_*-\psi\))-Ćirić-type contractive multivalued operators in b-metric spaces
en
en
In this paper we introduce the notion of (\(\alpha_*-\psi\))-Ćirić-type contractive multivalued operator and
investigate the existence and uniqueness of fixed point for such a mapping in b-metric spaces. The well-posedness of the fixed point problem and the Ulam-Hyres stability is also studied.
1165
1177
Monica-Felicia
Bota
Department of Mathematics
Babeş-Bolyai University
Romania
bmonica@math.ubbcluj.ro
Cristian
Chifu
Department of Busines
Babeş-Bolyai University
Romania
cristian.chifu@tbs.ubbcluj.ro
Erdal
Karapinar
Department of Mathematics
Atilim University
Turkey
erdalkarapinar@yahoo.com
\(\alpha_*-\psi\)-contractive multivalued operator
fixed point
b-metric space
well-posedness
Ulam-Hyers stability.
Article.43.pdf
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[1]
M. Ali, T. Kamran, On (\(\alpha_*,\psi\))-contractive multi-valued mappings, Fixed Point Theory Appl., 2013 (2013), 1-7
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M. Ali, T. Kamran, E. Karapinar , (\(\alpha,\psi,\xi\)) -contractive multi-valued mappings, Fixed Point Theory Appl., 2014 (2014), 1-8
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P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized \(\alpha-\psi\)-contractions, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math., 108 (2014), 519-526
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J. H. Asl, S. Rezapour, N. Shahzad , On fixed points of \(\alpha-\psi\)- contractive multifunctions, Fixed Point Theory Appl., 2012 (2012), 1-6
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V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, 1993 (1993), 1-7
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M. Berzig, E. Karapinar, Note on ''Modified \(\alpha-\psi\) -contractive mappings with application'', Thai J. Math., 13 (2015), 147-152
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M. F. Bota-Boriceanu, A. Petruşel, Ulam-Hyers stability for operatorial equations, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat., 57 (2011), 65-74
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E. Karapinar, B. Samet, Generalized \(\alpha-\psi\)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012), 1-17
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M. A. Kutbi, W. Sintunavarat , The existence of fixed point theorems via w-distance and \(\alpha-\)admissible mappings and applications, Abstr. Appl. Anal., 2013 (2013), 1-8
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V. L. Lazăr, Ulam-Hyers stability for partial differential inclusions, Electron. J. Qual. Theory Differ. Equ., 21 (2012), 1-19
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B. Mohammadi, S. Rezapour, N. Shahzad, Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 1-10
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I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 10 (2009), 305-320
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P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-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
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O. Yamaod, W. Sintunavarat, Fixed point theorems for \((\alpha-\beta )-( \psi-\varphi)\)-contractive mapping in b-metric spaces with some numerical results and applications, J. Nonlinear Sci. Appl., 9 (2016), 22-33
]
Equivalence of well-posedness between systems of hemivariational inequalities and inclusion problems
Equivalence of well-posedness between systems of hemivariational inequalities and inclusion problems
en
en
In this paper, we generalize the concept of well-posedness to a system of hemivariational inequalities in
Banach space. By introducing several concepts of well-posedness for systems of hemivariational inequalities
considered, we establish some metric characterizations of well-posedness and prove some equivalence results
of strong (generalized) well-posedness between a system of hemivariational inequalities and its derived system
of inclusion problems.
1178
1192
Yu-Mei
Wang
School of Mathematical Sciences
University of Electronic Science and Technology of China Chengdu
P. R. China
wymcyyx@163.com
Yi-Bin
Xiao
School of Mathematical Sciences
University of Electronic Science and Technology of China Chengdu
P. R. China
xiaoy9999@hotmail.com
Xing
Wang
School of Information Technology
Jiangxi University of Finance and Economics Nanchang
P. R. China
wangxing0793@163.com
Yeol Je
Cho
Department of Mathematics Education and the RINS
Center for General Education
Gyeongsang National University
China Medical University
Korea
Taiwan
yjchomath@gmail.com
System of hemivariational inequalities
well-posedness
Clarke's generalization gradient
system of inclusion problems.
Article.44.pdf
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]
Positive solutions for m-point boundary value problem
Positive solutions for m-point boundary value problem
en
en
In this paper, we study the existence of positive solutions for the following nonlinear m-point boundary
value problem for an increasing homeomorphism and homomorphism with sign changing nonlinearity:
\[
\begin{cases}
(\phi(u'))'+a(t) f(t,u(t))=0,\,\,\,\,\, 0<t<1,\\
u'(0)=\Sigma^{m-2}_{i=1}a_i
u'(\xi_i), \,\,u(1)=\Sigma^{k}_{i=1}b_i
u(\xi_i)- \Sigma^{s}_{i=k+1}b_i
u(\xi_i)-\Sigma^{m-2}_{i=s+1}b_i
u'(\xi_i), \end{cases}
\]
where \(\phi: R \rightarrow R\) is an increasing homeomorphism and homomorphism and \(\phi(0) = 0\). The nonlinear term
f may change sign. As an application, an example to demonstrate our results has given. The conclusions
in this paper essentially extend and improve the known results.
1193
1201
Hua
Su
School of economics
School of Mathematics and Quantitative Economics
Shandong University
Shandong University of Finance and Economics
China
China
jnsuhua@163.com
Xinjun
Wang
School of economics
Shandong University
China
showme1@yeah.net
m-point boundary value problem
positive solutions
fixed-point theorem.
Article.45.pdf
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]
Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay
Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay
en
en
In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and
a delay term. Under appropriate hypotheses on the relaxation function and the relationship between the
weight of the damping and the weight of the delay, we prove the well-posedness result by using Faedo-Galerkin method. By introducing suitable Lyapunov functionals, we establish a general decay result, from
which the exponential and polynomial types of decay are only special cases.
1202
1215
Danhua
Wang
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
China
matdhwang@yeah.net
Gang
Li
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
China
ligang@nuist.edu.cn
Biqing
Zhu
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
China
brucechu@163.com
Wave equation
transmission problem
general decay
viscoelastic term
delay.
Article.46.pdf
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[1]
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W. J. Liu, General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback, J. Math. Phys., 54 (2013), 1-9
##[15]
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##[16]
W. J. Liu, Arbitrary rate of decay for a viscoelastic equation with acoustic boundary conditions, Appl. Math. Lett., 38 (2014), 155-161
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W. J. Liu, K. W. Chen, Existence and general decay for nondissipative distributed systems with boundary frictional and memory dampings and acoustic boundary conditions, Z. Angew. Math. Phys., 66 (2015), 1595-1614
##[19]
W. J. Liu, K. W. Chen, J. Yu , Existence and general decay for the full von Kármán beam with a thermo-viscoelastic damping, frictional dampings and a delay term, IMA J. Math. Control Inform, (in press), -
##[20]
W. J. Liu, Y. Sun, General decay of solutions for a weak viscoelastic equation with acoustic boundary conditions, Z. Angew. Math. Phys., 65 (2014), 125-134
##[21]
A. Marzocchi, J. E. Muñoz Rivera, M. G. Naso, Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity, Math. Methods Appl. Sci., 25 (2002), 955-980
##[22]
S. A. Messaoudi, General decay of solutions of a viscoelastic equation, J. Math. Anal. Appl., 341 (2008), 1457-1467
##[23]
J. E. Muñoz Rivera, H. Portillo Oquendo, The transmission problem of viscoelastic waves, Acta Appl. Math., 62 (2000), 1-21
##[24]
S. Nicaise, C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim., 45 (2006), 1561-1585
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C. A. Raposo, The transmission problem for Timoshenko's system of memory type, Int. J. Mod. Math., 3 (2008), 271-293
##[26]
F. Tahamtani, A. Peyravi, Asymptotic behavior and blow-up of solutions for a nonlinear viscoelastic wave equation with boundary dissipation, Taiwanese J. Math., 17 (2013), 1921-1943
##[27]
S. T. Wu, Asymptotic behavior for a viscoelastic wave equation with a delay term, Taiwanese J. Math., 17 (2013), 765-784
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S. T. Wu , General decay of solutions for a nonlinear system of viscoelastic wave equations with degenerate damping and source terms, J. Math. Anal. Appl., 406 (2013), 34-48
]
A bilateral contact problem with adhesion and damage between two viscoelastic bodies
A bilateral contact problem with adhesion and damage between two viscoelastic bodies
en
en
This paper deals with the study of a mathematical model which describes the bilateral, frictionless
adhesive contact between two viscoelastic bodies with damage. The adhesion of the contact surfaces is con-
sidered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order
differential equation. We establish a variational formulation for the problem and prove the existence and
uniqueness result of the solution. The proofs are based on time-dependent variational equalities, a classical
existence and uniqueness result on parabolic equations, differential equations, and fixed-point arguments.
1216
1229
Ammar
Derbazi
Department of Mathematics, Faculty of MI
University Bachir El-Ibrahimi of Bordj Bou Arreridj
Algeria
ardazi@yahoo.com
Souida
Boukrioua
Department of Mathematics
University Kasdi Merbah of Ouargla
Algeria
sboukrioua@gmail.com
Mohamed
Dalah
Department of Mathematics, Faculty of Exact Sciences: FSE
University Mentouri of Constantine
Algeria
dalah.mohamed@yahoo.fr
Adel
Aissaoui
Department of Mathematics, Faculty of Exact Sciences
University Hamma Lakhdar
Algeria
aissaouiadel@gmail.com
Allaoua
Boudjedour
Department of Mathematics, Faculty of Exact Sciences: FSE
University Mentouri of Constantine
Algeria
aboudjedour@yahoo.com
Amar
Megrous
Department of Mathematics
EPSE-CSG of Constantine
Algeria
amegruos@yahoo.fr
Bilateral frictionless contact
adhesion
viscoelastic materials
fixed point
damage
weak solution.
Article.47.pdf
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[1]
A. Aissaoui, N. Hemici , Bilateral contact problem with adhesion and damage, Electron. J. Qual. Theory Differ. Equ., 2014 (2014), 1-16
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]
On fixed soft element theorems in se-uniform spaces
On fixed soft element theorems in se-uniform spaces
en
en
First we introduce a new structure of uniform spaces, called se-uniform spaces, and provide some of
their basic properties. Next, we present the notion of a soft E-distance in se-uniform spaces, which is a
soft version of E-distance of Aamri and El Moutawakil [M. Aamri, D. El Moutawakil, Acta Math. Acad.
Peadegog. Nyhazi., 20 (2004), 83-91]. Then, by using the soft E-distance, we establish some fixed soft
element theorems for various mappings on se-uniform spaces, which are the main results of the paper. This
is the first kind of such results in this direction.
1230
1242
İzzettin
Demir
Department of Mathematics
Duzce University
Turkey
izzettindemir@duzce.edu.tr
Oya Bedre
Özbakır
Department of Mathematics
Ege University
Turkey
oya.ozbakir@ege.edu.tr
İsmet
Yıldız
Department of Mathematics
Duzce University
Turkey
ismetyildiz@duzce.edu.tr
Soft order
se-uniform space
soft E-distance
fixed soft element.
Article.48.pdf
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[1]
M. Aamri, D. El Moutawakil , Common fixed point theorems for E-contractive or E-expansive maps in uniform spaces, Acta Math. Acad. Peadegog. Nyhazi., 20 (2004), 83-91
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Inverse problems for a nonlocal wave equation with an involution perturbation
Inverse problems for a nonlocal wave equation with an involution perturbation
en
en
Two inverse problems for the wave equation with involution are considered. Results on existence and
uniqueness of solutions of these problems are presented.
1243
1251
Mokhtar
Kirane
NAAM Research Group, Department of Mathematics, Faculty of Science
Laboratoire de Mathematiques, Image et Applications, Pole Sciences et Technologies
King Abdulaziz University
Universite de La Rochelle, A. M. Crepeau
Saudi Arabia
France
mokhtar.kirane@univ-lr.fr
Nasser
Al-Salti
Department of Mathematics and Statistics, College of Science
Sultan Qaboos University
Oman
nalsalti@squ.edu.om
Inverse problem
nonlocal wave equation
involution perturbation.
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On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function
On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function
en
en
In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with
respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals
and the Hadamard fractional integrals.
1252
1260
Mohamed
Jleli
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Hermite-Hadamard inequality
fractional integral with respect to another function
Riemann-Liouville fractional integral
Hadamard fractional integral.
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]
Difference-genetic co-evolutionary algorithm for nonlinear mixed integer programming problems
Difference-genetic co-evolutionary algorithm for nonlinear mixed integer programming problems
en
en
In this paper, the difference genetic co-evolutionary algorithm (D-GCE) is proposed for the mixed integer
programming problems. First, the mixed integer programming problem with constrains converted to
unconstrained bi-objective optimization problems. Secondly, selection mechanism combines the Pareto dominance
and superiority of feasible solution methods to choose the excellent individual as the next generation.
Final, differential evolution algorithm and genetic algorithm handle the continuous part and discrete part,
respectively. Numerical experiments on 24 test functions have shown that the new approach is efficient.
The comparison results among the D-GCE and other evolutionary algorithms indicate that the proposed
D-GCE algorithm is competitive with and in some cases superior to, other existing algorithms in terms of
the quality, efficiency, convergence rate, and robustness of the final solution.
1261
1284
Yuelin
Gao
Institute of Information and System Science
School of Computer Science and Information Engineering
Beifang University of Nationalities
Hefei University of Technology
China
China
gaoyuelin@263.net
Ying
Sun
School of Computer Science and Information Engineering
Hefei University of Technology
China
nxsunying@126.com
Jun
Wu
Institute of Information and System Science
Beifang University of Nationalities
China
wujunmath@163.com
Mixed integer programming
differential evolution
genetic algorithm
co-evolution
constrained optimization.
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Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms
Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms
en
en
This paper is concerned with the existence and exponential stability of anti-periodic solutions of a neutral
BAM neural network with time-varying delays in the leakage terms. Using some analysis skills and Lyapunov
method, a series of sufficient conditions for the existence and exponential stability of anti-periodic solutions
to the neutral BAM neural networks with time-varying delays in the leakage terms are presented. Our
results are new and complement some previously known ones.
1285
1305
Changjin
Xu
Guizhou Key Laboratory of Economics System Simulation Guizhou
University of Finance and Economics
China
xcj403@126.com
Peiluan
Li
School of Mathematics and Statistics
Henan University of Science and Technology
China
lpllpl_lpl@163.com
Neutral BAM neural network
anti-periodic solution
exponential stability
time-varying delay
leakage term.
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Z. Q. Zhang, D. M. Zhou, Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks, J. Franklin Inst., 347 (2010), 763-780
]
New Higher Order Multi-step Methods for Solving Scalar Equations (RETRACTED PAPER)
New Higher Order Multi-step Methods for Solving Scalar Equations (RETRACTED PAPER)
en
en
We introduce and analyze two new multi-step iterative methods with convergence order four and five
based on modified homotopy perturbation methods, using the system of coupled equations involving an
auxiliary function. We also present the convergence analysis and various numerical examples to demonstrate
the validity and efficiency of our methods. These methods are a good addition and also a generalization of
the existing methods for solving nonlinear equations.
1306
1315
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Faisal
Ali
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Pakistan
faisalali@bzu.edu.pk
Arif
Rafiq
Department of Mathematics and Statistics
Virtual University of Pakistan
Pakistan
iq@gmail.com
Muhammad Asgher
Taher
Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Pakistan
asghartahir99@gmail.com
Young Chel
Kwund
Department of Mathematics
Dong-A University
Korea
yckwun@dau.ac.kr
Iterative methods
nonlinear equations
order of convergence
auxiliary function
modified homotopy method.
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Note on Aczel-type inequality and Bellman-type inequality
Note on Aczel-type inequality and Bellman-type inequality
en
en
In this short note, by using the method of Vasić and Pečarić [P. M. Vasić, J. E. Pečarić, Mathematica Rev.
D'Anal. Num. Th. L'Approx., 25 (1982), 95-103], we obtain some properties of Aczél-type inequality and
Bellman-type inequality, and then we obtain some new refinements of Aczél-type inequality and Bellmantype
inequality.
1316
1322
Jing-Feng
Tian
College of Science and Technology
North China Electric Power University
P. R. China
tianjfhxm_ncepu@163.com
Yi-Jun
Zhou
No.1 High School of Baoding
Hebei Province
P. R. China
632404212@qq.com
Aczél-type inequality
Bellman-type inequality
refinement
property.
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Strong convergence of hybrid algorithms for fixed point and bifunction equilibrium problems in reflexive Banach spaces
Strong convergence of hybrid algorithms for fixed point and bifunction equilibrium problems in reflexive Banach spaces
en
en
Fixed point and bifunction equilibrium problems are studied via hybrid algorithms. Strong convergence
theorems are established in the framework of re
exive Banach spaces. The results presented in this paper
improve the corresponding results announced by many authors recently.
1323
1333
Lingmin
Zhang
Institute of Mathematics and Information Technology
Hebei Normal University of Science and Technology
China
zhanglm103@126.com
Xinbin
Li
Key Lab of Industrial Computer Control Engineering of Hebei Province
Yanshan University
China
Asymptotically quasi-\(\phi\)-nonexpansive mapping
equilibrium problem
fixed point
generalized projection.
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Y. Liu, Convergence theorems for a generalized equilibrium problem and two asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Funct. Anal. Appl., 19 (2014), 317-328
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B. Liu, C. Zhang, Strong convergence theorems for equilibrium problems and quasi-\(\phi\)-nonexpansive mappings, Nonlinear Funct. Anal. Appl., 16 (2011), 365-385
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J. Y. Wang, M. Ehrgott, Modelling route choice behaviour in a tolled road network with a time surplus maximisation bi-objective user equilibrium model , Transp. Res., 57 (2013), 342-360
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H. Zegeye, N. Shahzad, Strong convergence theorem for a common point of solution of variational inequality and fixed point problem, Adv. Fixed Point Theory, 2 (2012), 374-397
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L. Zhang, Y. Hao , Fixed point methods for solving solutions of a generalized equilibrium problem, J. Nonlinear Sci. Appl., 9 (2016), 149-159
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L. Zhang, H. Tong , An iterative method for nonexpansive semigroups, variational inclusions and generalized equilibrium problems, Adv. Fixed Point Theory, 4 (2014), 325-343
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J. Zhao , Strong convergence theorems for equilibrium problems, fixed point problems of asymptotically nonexpansive mappings and a general system of variational inequalities , Nonlinear Funct. Anal. Appl., 16 (2011), 447-464
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J. Zhao, Approximation of solutions to an equilibrium problem in a nonuniformly smooth Banach space, J. Inequal. Appl., 2013 (2013), 1-10
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L. C. Zhao, S. S. Chang, Strong convergence theorems for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Nonlinear Sci. Appl., 2 (2009), 78-91
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H. Zhou, G. Gao, B. Tan, Convergence theorems of a modified hybrid algorithm for a family of quasi-\(\phi\)- asymptotically nonexpansive mappings, J. Appl. Math. Comput., 32 (2010), 453-464
]
Analytic and loop solutions for the K(2,2) equation (focusing branch)
Analytic and loop solutions for the K(2,2) equation (focusing branch)
en
en
In this paper, we study analytic and loop solutions of the K(2,2) equation(focusing branch), which is
first proposed by Rosenau. The implicit analytic and loop solutions are obtained by using the dynamical
system approach. Moreover, we investigate how the famous Rosenau-Hyman compactons can be recovered
as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical
system by theoretical analysis and numerical simulation.
1334
1340
Chunhai
Li
School of Mathematics and Computing Science and Guangxi Experiment Center of Information Science
Guilin University of Electronic Technology
P. R. China
chunhaili@guet.edu.cn
Shengqiang
Tang
School of Mathematics and Computing Science and Guangxi Experiment Center of Information Science
Guilin University of Electronic Technology
P. R. China
tangsq@guet.edu.cn
Zhongjun
Ma
School of Mathematics and Computing Science and Guangxi Experiment Center of Information Science
Guilin University of Electronic Technology
P. R. China
mazhongjun@guet.edu.cn
Loop solution
peakon
compacton
solitary wave
K(2،2) equation.
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Local conjugacy theorems for \(C^1\) operators between Banach manifolds
Local conjugacy theorems for \(C^1\) operators between Banach manifolds
en
en
In this paper, by the generalized inverse theory of bounded linear operators, the local conjugacy theorem
for \(C^1\) operators between Banach manifolds is established. According to this theorem, the conditions which
can be used to make sure that a \(C^1\) operator can be linearized are provided. Local conjugacy theorems for
nonlinear Fredholm operators, nonlinear semi-Fredholm operators and finite rank operators are introduced.
1341
1348
Qiang
Li
School of Mathematics and Statistics
School of Science
Northeast Normal University
Qiqihar University
P. R. China
P. R. China
liq347@nenu.edu.cn
Donghe
Pei
School of Science
Qiqihar University
P. R. China
peidh340@nenu.edu.cn
Conjugacy theorem
generalized inverse
linearization
Banach manifold.
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N. Castro-González, J. Y. Vélez-Cerrada, On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces, J. Math. Anal. Appl., 341 (2008), 1213-1223
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Generalized Kudryashov method for nonlinear fractional double sinh--Poisson equation
Generalized Kudryashov method for nonlinear fractional double sinh--Poisson equation
en
en
Using the generalized Kudryashov method (GKM), we derive exact solutions of the nonlinear fractional
double sinh-Poisson equation. We obtain novel dark soliton solutions. Some numerical simulations were
done to see the behavior of these solutions.
1349
1355
Seyma Tuluce
Demiray
Department of Mathematics
Firat University
Turkey
seymatuluce@gmail.com
Hasan
Bulut
Department of Mathematics
Firat University
Turkey
hbulut@firat.edu.tr
Nonlinear fractional double sinh-Poisson equation
generalized Kudryashov method
travelling wave transformation
dark soliton solution.
Article.58.pdf
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A. Atangana, S. Tuluce Demiray, H. Bulut, Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus, Abstr. Appl. Anal., 2014 (2014), 1-7
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T. Bartsch, A. Pistoia, T. Weth, N-vortex equilibria for ideal fluids in bounded planar domains and new nodal solutions of the sinh-Poisson and the Lane-Emden-Fowler equations , Commun. Math. Phys., 297 (2010), 653-686
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A. Biswas, A. H. Bhrawy, M. A. Abdelkawy, A. A. Alshaery, E. M. Hilal, Symbolic Computation of Some Nonlinear Fractional Differential Equations, Rom. J. Phys., 59 (2014), 433-442
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H. Bulut , Classification of exact solutions for generalized form of K(m,n) equation, Abstr. Appl. Anal., 2013 (2013), 1-11
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H. Bulut, Y. Pandir, S. Tuluce Demiray, Exact Solutions of Time-Fractional KdV Equations by Using Generalized Kudryashov Method, Internat. J. Modeling Optim., 4 (2014), 315-320
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H. Bulut, S. Tuluce Demiray, M. Kayhan, The Approximate Solutions Of Time-Fractional Diffusion Equation By Using Crank Nicholson Method, Acta Univ. Apulensis, 40 (2014), 103-112
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S. Tuluce Demiray, Y. Pandir, H. Bulut , Generalized Kudryashov Method for Time-Fractional Differential Equations , Abstr. Appl. Anal., 2014 (2014), 1-13
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S. Tuluce Demiray, Y. Pandir, H. Bulut , The investigation of exact solutions of nonlinear time-fractional Klein-Gordon equation by using generalized Kudryashov method, AIP Conference Proc., 1637 (2014), 283-289
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S. Tuluce Demiray, Y. Pandir, H. Bulut , The Analysis of The Exact Solutions of The Space Fractional Coupled KD Equations, AIP Conference Proc., 1648 (2015), 1-5
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]
Quasilinearization method for nonlinear differential equations with causal operators
Quasilinearization method for nonlinear differential equations with causal operators
en
en
Employing quasilinearization technique coupled with the method of upper and lower solutions, we construct
monotone sequences whose iterates are solutions to corresponding linear problems and show that
the sequences converge uniformly and monotonically to the unique solution of the nonlinear problem with
causal operator. Especially, instead of assuming convexity or concavity assumption on the nonlinear term
that is demanded by the method of quasilinearization, we impose weaker conditions to be more useful in
applications. The results obtained include several special cases and extend previous results.
1356
1364
Ali
Yakar
Department of Mathematics
Gaziosmanpasa University
Turkey
ali.yakar@gop.edu.tr
Mehmet Emir
Koksal
Department of Mathematics
Ondokuz Mayis University
Turkey
mekoksal@omu.edu.tr
Quasilinearization
differential equation
causal operator
nonlinearity
initial value problem
quadratic convergence.
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A new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces
A new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces
en
en
Sufficient conditions for the convergence of a new multistep iteration to a common fixed point of a
finite family of asymptotically quasi-nonexpansive mappings in the framework of convex metric spaces are
obtained. As an application, related results for a new three step iteration are derived. Our convergence
results generalize and refine many known results.
1365
1372
Birol
Gunduz
Department of Mathematics, Faculty of Science and Art
Erzincan University
Turkey
birolgndz@gmail.com
Iteration process
convex metric spaces
asymptotically quasi-nonexpansive mappings
common fixed point
strong convergence.
Article.60.pdf
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B. Gunduz, S. Akbulut, Strong and \(\Delta\)-convergence theorems in hyperbolic spaces, Miskolc Math. Notes, 14 (2013), 915-925
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Fixed point results for multivalued contractive type maps
Fixed point results for multivalued contractive type maps
en
en
Using generalized distance in metric spaces, we prove some fixed point results for multivalued generalized
contractive type maps. Consequently, several known fixed point results are either improved or generalized.
An interesting example in support of the result is also presented.
1373
1381
Saleh Abdullah
Al-Mezel
Department of Mathematics
King Abdulaziz University
Saudi Arabia
salmezel@kau.edu.sa
Metric space
fixed point
contractive multi-valued map
w-distance
u-distance.
Article.61.pdf
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]
Qualitative behavior of vector-borne disease model
Qualitative behavior of vector-borne disease model
en
en
We investigate some qualitative behavior of a vector-borne disease model. Specially, we study local as
well as global asymptotic stability of both disease-free and endemic equilibria of the model under certain
parametric conditions. Furthermore, global behavior of disease-free equilibrium is investigated by constructing
Lyapunov function, while global behavior of endemic equilibrium is discussed through geometric
approach. Numerical simulations are provided to illustrate the theoretical discussion.
1382
1395
Muhammad
Ozair
Department of Mathematics
The University of Poonch Rawalakot
Pakistan
ozairmuhammad@gmail.com
Qamar
Din
Department of Mathematics
The University of Poonch Rawalakot
Pakistan
qamar.sms@gmail.com
Takasar
Hussain
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
htakasarnust@gmail.com
Aziz Ullah
Awan
Department of Mathematics
University of the Punjab
Pakistan
aziz.math@pu.edu.pk
Vector-borne model
steady-states
stability analysis.
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]
A new kind of generalized fuzzy integrals
A new kind of generalized fuzzy integrals
en
en
Fuzzy integral is an important tool to study fuzzy differential equations. Under normal circumstances,
there are two basic limitations: limited of integral interval and boundedness of integrand. However, in
practical problems, it is dificult to calculate when integral interval is not common interval. Then fuzzy
integral on infinite interval is taken into consideration. In this paper, definition of a kind of generalized Liu
integral is given. Moreover, properties and theorems of this kind of generalized fuzzy integral are obtained.
1396
1401
Cuilian
You
College of Mathematics and Information Science
Hebei University
China
yycclian@163.com
Hongyan
Ma
College of Mathematics and Information Science
Hebei University
China
mahongyan@hbu.edu.cn
Huae
Huo
College of Mathematics and Information Science
Hebei University
China
huohuaehehe@163.com
Fuzzy variable
fuzzy process
Liu process
generalized fuzzy integral.
Article.63.pdf
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[1]
X. Chen, Z. Qin, A new existence and uniqueness theorem for fuzzy differential equation , Int. J. Fuzzy Syst., 13 (2011), 148-151
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X. Li, B. Liu, A sufficent and necessary condition for credibility measures, Int. J. Uncertainty, Fuzziness & Knowledge-Based Syst., 14 (2006), 527-535
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C. You, H. Huo, W. Wang, Multi-dimensional Liu process, differential and integral , J. East Asian Math., 29 (2013), 13-22
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Generalized vector equilibrium problems on Hadamard manifolds
Generalized vector equilibrium problems on Hadamard manifolds
en
en
In this paper, we study several types of Generalized Vector Equilibrium Problems (GVEP) on Hadamard
manifolds. We prove sufficient conditions under which the solution set of (GVEP)'s is nonempty. As an
application, we prove existence theorems for the system of generalized vector variational inequality problems
and the system of generalized Pareto optimization problems.
1402
1409
Shreyasi
Jana
Department of Mathematics
Indian Institute of Technology Kharagpur
India
shreyasi.iitkgp@gmail.com
Chandal
Nahak
Department of Mathematics
Indian Institute of Technology Kharagpur
India
cnahak@maths.iitkgp.ernet.in
Cristiana
Ionescu
Department of Mathematics and Informatics
University Politehnica of Bucharest
Romania
cristianaionescu58@yahoo.com
Hadamard manifold
variational inequality
equilibrium problem
KKM mapping.
Article.64.pdf
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