]>
2017
10
5
ISSN 2008-1898
576
Infinitely many nontrivial solutions for fractional boundary value problems with impulses and perturbation
Infinitely many nontrivial solutions for fractional boundary value problems with impulses and perturbation
en
en
By the variational methods, the existence criteria of infinitely many nontrivial solutions for fractional differential equations
with impulses and perturbation are established. An example is given to illustrate main results. Recent results in the literature
are generalized and improved.
2283
2295
Peiluan
Li
Control science and engineering post-doctoral mobile stations
School of Mathematics and Statistics
Henan University of Science and Technology
Henan University of Science and Technology
China
China
lpllpl_lpl@163.com
Jianwei
Ma
College of Information Engineering
Henan University of Science and Technology
China
Lymjw@163.com
Hui
Wang
College of Information Engineering
Henan University of Science and Technology
China
wh@haust.edu.cn
Zheqing
Li
Network and Information Center
Henan University of Science and Technology
China
lzq@haust.edu.cn
Fractional differential equations with impulses and perturbation
infinitely many nontrivial solutions
variational methods.
Article.1.pdf
[
[1]
C.-Z. Bai, Existence of three solutions for a nonlinear fractional boundary value problem via a critical points theorem, Abstr. Appl. Anal., 2012 (2012), 1-13
##[2]
D. Baleanu, H. Khan, H. Jafari, R. A. Khan, M. Alipour, On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions, Adv. Difference Equ., 2015 (2015), 1-14
##[3]
M. Benchohra, J. Henderson, S. Ntouyas, Impulsive differential equations and inclusions, Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York (2006)
##[4]
G. Bonanno, A critical point theorem via the Ekeland variational principle, Nonlinear Anal., 75 (2012), 2992-3007
##[5]
G. Bonanno, S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., 89 (2010), 1-10
##[6]
G. Bonanno, R. Rodríguez-López, S. Tersian, Existence of solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 717-744
##[7]
J. Chen, X. H. Tang, Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory, Abstr. Appl. Anal., 2012 (2012), 1-21
##[8]
J.-N. Corvellec, V. V. Motreanu, C. Saccon, Doubly resonant semilinear elliptic problems via nonsmooth critical point theory, J. Differential Equations, 248 (2010), 2064-2091
##[9]
G. D'Aguì, B. Di Bella, S. Tersian, Multiplicity results for superlinear boundary value problems with impulsive effects, Math. Methods Appl. Sci., 39 (2016), 1060-1068
##[10]
A. Debbouche, D. Baleanu, Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems, Comput. Math. Appl., 62 (2011), 1442-1450
##[11]
V. J. Erwin, J. P. Roop, Variational formulation for the stationary fractional advection dispersion equation, Numer. Methods Partial Differential Equations, 22 (2006), 558-576
##[12]
M. A. Firoozjaee, S. A. Yousefi, H. Jafari, D. Baleanu, On a numerical approach to solve multi-order fractional differential equations with initial/boundary conditions, J. Comput. Nonlinear Dynam., 10 (2015), 1-6
##[13]
B. Ge, Multiple solutions for a class of fractional boundary value problems, Abstr Appl. Anal., 2012 (2012), 1-16
##[14]
Z.-G. Hu, W.-B. Liu, J.-Y. Liu, Ground state solutions for a class of fractional differential equations with Dirichlet boundary value condition, Abstr. Appl. Anal., 2014 (2014), 1-7
##[15]
F. Jiao, Y. Zhou, Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl., 62 (2011), 1181-1199
##[16]
F. Jiao, Y. Zhou, Existence results for fractional boundary value problem via critical point theory, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 22 (2012), 1-17
##[17]
H. Khalil, R. A. Khan, D. Baleanu, S. H. Saker, Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions, Adv. Difference Equ., 1 (2016), 1-28
##[18]
A. A. Kilbas, M. H. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[19]
V. Lakshmikantham, D. D. Baınov, P. S. Simeonov, Theory of impulsive differential equations, Series in Modern Applied Mathematics, World Scientific Publishing Co., Inc., Teaneck, NJ (1989)
##[20]
V. Lakshmikantham, S. Leela, D. J. Vasundhara, Theory of fractional dynamic systems, Cambridge Scientific Publishers, Cambridge, UK (2009)
##[21]
Y.-N. Li, H.-R. Sun, Q.-G. Zhang, Existence of solutions to fractional boundary-value problems with a parameter, Electron. J. Differential Equations, 2013 (2013), 1-12
##[22]
J. Mawhin, M. Willem, Critical point theory and Hamiltonian systems, Applied Mathematical Sciences, Springer- Verlag, New York (1989)
##[23]
N. Nyamoradi, R. Rodríguez-López, On boundary value problems for impulsive fractional differential equation, Appl. Math. Comput., 271 (2015), 874-892
##[24]
P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (1986)
##[25]
R. Rodríguez-López, S. Tersian, Multiple solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 1016-1038
##[26]
A. M. Samoilenko, N. A. Perestyuk, Impulsive differential equations, With a preface by Yu. A. Mitropolskiıand a supplement by S. I. Trofimchuk, Translated from the Russian by Y. Chapovsky, World Scientific Series on Nonlinear Science, Series A: Monographs and Treatises, World Scientific Publishing Co., Inc., River Edge, NJ (1995)
##[27]
H.-R. Sun, Q.-G. Zhang, Existence of solutions for a fractional boundary value problem via the Mountain Pass method and an iterative technique, Comput. Math. Appl., 64 (2012), 3436-3443
##[28]
Y. Tian, W.-G. Ge, Multiple solutions of impulsive Sturm-Liouville boundary value problem via lower and upper solutions and variational methods, J. Math. Anal. Appl., 387 (2012), 475-489
##[29]
C. Torres, Mountain pass solution for a fractional boundary value problem, J. Fract. Calc. Appl., 5 (2014), 1-10
##[30]
X.-J. Yang, Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems, ArXiv, 2016 (2016), 1-13
##[31]
X.-J. Yang, D. Baleanu, Y. Khan, S. T. Mohyud-Din, Local fractional variational iteration method for diffusion and wave equations on Cantor sets, Romanian J. Phys., 59 (2014), 36-48
##[32]
X.-J. Yang,, F. Gao, J. A. Tenreiro Machado, D. Baleanu, A new fractional derivative involving the normalized sinc function without singular kernel, ArXiv, 2017 (2017), 1-11
##[33]
X.-J. Yang, H. M. Srivastava, J. A. Tenreiro Machado, A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow, Therm. Sci., 20 (2016), 753-756
##[34]
X.-J. Yang, J. A. Tenreiro Machado, A new fractional operator of variable order: application in the description of anomalous diffusion, ArXiv, 2016 (2016), 1-13
##[35]
X.-J. Yang, J. A. Tenreiro Machado, D. Baleanu, C. Cattani, On exact traveling-wave solutions for local fractional Korteweg-de Vries equation, Chaos, 26 (2016), 1-5
##[36]
Y.-L. Zhao, H.-B. Chen, B. Qin, Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods, Appl. Math. Comput., 257 (2015), 417-427
##[37]
Y.-L. Zhao, Y.-L. Zhao, Nontrivial solutions for a class of perturbed fractional differential systems with impulsive effects, Bound. Value Probl., 2016 (2016), 1-16
##[38]
Y. Zhou, Basic theory of fractional differential equations, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2014)
##[39]
W.-M. Zou, Variant fountain theorems and their applications, Manuscripta Math., 104 (2001), 343-358
]
Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems for some contractive mappings in \(M_s\)-metric spaces
Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems for some contractive mappings in \(M_s\)-metric spaces
en
en
In this paper, first, we introduce several types of the Ulam-Hyers stability, the well-posedness and the limit shadowing
property of fixed point problems in \(M_s\)-metric spaces. Second, we give such results for fixed point problems of Banach and
Kannan contractive mappings in \(M_s\)-metric spaces. Finally, we give some examples to illustrate the validity of our main results.
2296
2308
Mi
Zhou
School of Science and Technology
Sanya College
China
mizhou330@126.com
Xiao-lan
Liu
College of Science
Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing
Sichuan University of Science and Engineering
China
China
stellalwp@163.com
Yeol Je
Cho
Department of Mathematics Education
enter for General Education
Gyeongsang National University
China Medical University
Korea
Taiwan
yjcho@gnu.ac.kr
Boško
Damjanovic
Faculty of Agriculture
University of Belgrade
Serbia
dambo@agrif.bg.ac.rs
Fixed point problem
Ulam-Hyers stability
well-posedness
limit shadowing property
\(M_s\)-metric spaces.
Article.2.pdf
[
[1]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[2]
M. F. Bota, E. Karapınar, O. Mleşniţe, Ulam-Hyers stability results for fixed point problems via \(\alpha-\psi\)-contractive mapping in (b)-metric space, Abstr. Appl. Anal., 2013 (2013), 1-6
##[3]
M. F. Bota-Boriceanu, A. Petruşel, Ulam-Hyers stability for operatorial equations, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 57 (2011), 65-74
##[4]
F. S. De Blasi, J. Myjak, Sur la porosité de l’ensemble des contractions sans point fixe, (French) [[On the porosity of the set of contractions without fixed points]] C. R. Acad. Sci. Paris Sér. I Math., 308 (1989), 51-54
##[5]
R. Kannan , Some results on fixed points, II, Amer. Math. Monthly, 76 (1969), 405-408
##[6]
B. K. Lahiri, P. Das, Well-posedness and porosity of a certain class of operators, Demonstratio Math., 38 (2005), 169-176
##[7]
N. M. Mlaiki, A contraction principle in partial S-metric spaces, Univers. J. Math. Math. Sci., 5 (2014), 109-119
##[8]
N. M. Mlaiki, N. Souayah, K. Abodayeh, T. Abdeljawad, Contraction principles inMs-metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 575-582
##[9]
A. Pansuwan, W. Sintunavarat, J. Y. Choi, Y. J. Cho, Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems in M-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 4489-4499
##[10]
S. Reich, A. J. Zaslavski, Well-posedness of fixed point problems, Far East J. Math. Sci. (FJMS), Special Volume, Part III, (2001), 393-401
##[11]
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64 (2012), 258-266
##[12]
P. V. Subrahmanyam, Completeness and fixed-points, Monatsh. Math., 80 (1975), 325-330
]
Improved conditions for neutral delay systems with novel inequalities
Improved conditions for neutral delay systems with novel inequalities
en
en
This paper studies the stability problem of a class of neutral delay systems. It firstly establishes two novel integral inequalities,
which are better than the same type inequalities found in the literature. Then it derives, by using the new inequalities
and the Lyapunov functional method, some sufficient delay-dependent conditions for asymptotic stability of the neutral delay
systems. Three numerical examples are provided to illustrate the advantage and effectiveness of the obtained results.
2309
2317
L. L.
Xiong
School of Mathematics and Computer Science
Yunnan Minzu University
China
lianglin-5418@126.com
J.
Cheng
School of Science
Hubei University for Nationalities
China
jcheng6819@126.com
X. Z.
Liu
Department of Applied Mathematics
University of Waterloo
Canada N2L 3G1
xinzhi.liu@uwaterloo.ca
T.
Wu
School of Mathematics and Computer Science
Yunnan Minzu University
China
1175908375@qq.com
New integral inequality
neutral delay system
delay-dependent stability
Lyapunov functional.
Article.3.pdf
[
[1]
Y.-G. Chen, S.-M. Fei, Z. Gu, Y.-M. Li, New mixed-delay-dependent robust stability conditions for uncertain linear neutral systems, IET Control Theory Appl., 8 (2014), 606-613
##[2]
L.-M. Ding, Y. He, M. Wu, C.-Y. Ning, Improved mixed-delay-dependent asymptotic stability criteria for neutral systems, IET Control Theory Appl., 9 (2015), 2180-2187
##[3]
M. Fang, J. H. Park, A multiple integral approach to stability of neutral time-delay systems, Appl. Math. Comput., 224 (2013), 714-718
##[4]
E. Fridman, U. Shaked, Delay-dependent stability and \(H_\infty\) control: constant and time-varying delays, Internat. J. Control, 76 (2003), 48-60
##[5]
Q.-L. Han, Robust stability of uncertain delay-differential systems of neutral type, Automatica J. IFAC, 38 (2002), 719-723
##[6]
Q.-L. Han, On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty, Automatica J. IFAC, 40 (2004), 1087-1092
##[7]
Q.-L. Han, On stability of linear neutral systems with mixed time delays: a discretized Lyapunov functional approach, Automatica J. IFAC, 41 (2005), 1209-1218
##[8]
Y. He, Q.-G. Wang, C. Lin, M. Wu, Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems, Internat. J. Robust Nonlinear Control, 15 (2005), 923-933
##[9]
Y. He, M. Wu, J.-H. She, G.-P. Liu, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems Control Lett., 51 (2004), 57-65
##[10]
C.-Y. Kao, A. Rantzer, Stability analysis of systems with uncertain time-varying delays, Automatica J. IFAC, 43 (2007), 959-970
##[11]
X.-G. Li, X.-J. Zhu, A. Cela, A. Reama, Stability analysis of neutral systems with mixed delays, Automatica J. IFAC, 44 (2008), 2968-2972
##[12]
X.-G. Liu, M. Wu, R. Martin, M.-L. Tang, Stability analysis for neutral systems with mixed delays, J. Comput. Appl. Math., 202 (2007), 478-497
##[13]
P. G. Park, W. I. Lee, S Y. Lee, Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, J. Franklin Inst., 352 (2015), 1378-1396
##[14]
M. N. A. Parlakçi, Robust stability of uncertain neutral systems: a novel augmented Lyapunov functional approach, IET Control Theory Appl., 1 (2007), 802-809
##[15]
W. Qian, J. Liu, Y.-X. Sun, S.-M. Fei, A less conservative robust stability criteria for uncertain neutral systems with mixed delays, Math. Comput. Simulation, 80 (2010), 1007-1017
##[16]
J. Sun, G. P. Liu, On improved delay-dependent stability criteria for neutral time-delay systems, Eur. J. Control, 15 (2009), 613-623
##[17]
J. Sun, G. P. Liu, J. Chen, Delay-dependent stability and stabilization of neutral time-delay systems, Internat. J. Robust Nonlinear Control, 19 (2009), 1364-1375
##[18]
M. Wu, Y. He, J.-H. She, New delay-dependent stability criteria and stabilizing method for neutral systems, IEEE Trans. Automat. Control, 49 (2004), 2266-2271
##[19]
L.-L. Xiong, H.-Y. Zhang, Y.-K. Li, Z.-X. Liu, Improved stabilization criteria for neutral time-delay systems, Math. Probl. Eng., 2016 (2016), 1-13
##[20]
D. Yue, Q.-L. Han, A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model, IEEE Trans. Circuits Syst. II, Exp. Briefs, 51 (2004), 685-689
##[21]
H.-B. Zeng, Y. He, M. Wu, J.-H. She, Free-matrix-based integral inequality for stability analysis of systems with timevarying delay, IEEE Trans. Automat. Control, 60 (2015), 2768-2772
##[22]
H.-B. Zeng, Y. He, M. Wu, J.-H. She, New results on stability analysis for systems with discrete distributed delay, Automatica J. IFAC, 60 (2015), 189-192
##[23]
N. Zhao, C. Lin, B. Chen, Q.-G. Wang, A new double integral inequality and application to stability test for time-delay systems, Appl. Math. Lett., 65 (2017), 26-31
]
Weak \(\theta-\phi-\)contraction and discontinuity
Weak \(\theta-\phi-\)contraction and discontinuity
en
en
In this paper, we introduce the notion of weak \(\theta-\phi-\)contraction ensuring a convergence of successive approximations but
does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised
by Rhoades in [B. E. Rhoades, Fixed point theory Appl, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence,
RI, 72 (1988), 233–245].
2318
2323
Dingwei
Zheng
College of Mathematics and Information Science
Guangxi University
P. R. China
dwzheng@gxu.edu.cn
Pei
Wang
School of Mathematics and Information Science
Yulin Normal University
P. R. China
274958670@qq.com
Fixed point
discontinuity
weak \(\theta-\phi-\)contraction.
Article.4.pdf
[
[1]
R. K. Bisht, R. P. Pant, A remark on discontinuity at fixed point, J. Math. Anal. Appl., 445 (2017), 1239-1241
##[2]
F. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901
##[3]
L. Ćirić, M. Abbas, R. Saadati, N. Hussain, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., 217 (2011), 5784-5789
##[4]
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
##[5]
R. Kannan, Some results on fixed points, II, Amer. Math. Monthly, 76 (1969), 405-408
##[6]
R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl., 240 (1999), 284-289
##[7]
H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
##[8]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2003), 1435-1443
##[9]
B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257-290
##[10]
B. E. Rhoades, Contractive definitions and continuity, Fixed point theory and its applications, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, 72 (1988), 233-245
##[11]
A. F. Roldán-López de Hierro, N. Shahzad, New fixed point theorem under R-contractions, Fixed Point Theory Appl., 2015 (2015), 1-18
##[12]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\) -contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[13]
T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317
##[14]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-6
##[15]
D.-W. Zheng, Z.-Y. Cai, P. Wang, New fixed point theorems for \(\theta-\phi-\)contraction in complete metric spaces, , (Preprint), -
]
Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients
Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients
en
en
In this paper, Whitham–Broer–Kaup (WBK) equations with time-dependent coefficients are exactly solved through Hirota’s
bilinear method. To be specific, the WBK equations are first reduced into a system of variable-coefficient Ablowitz–Kaup–
Newell–Segur (AKNS) equations. With the help of the AKNS equations, bilinear forms of the WBK equations are then given.
Based on a special case of the bilinear forms, new one-soliton solutions, two-soliton solutions, three-soliton solutions and the
uniform formulae of n-soliton solutions are finally obtained. It is graphically shown that the dynamical evolutions of the
obtained one-, two- and three-soliton solutions possess time-varying amplitudes in the process of propagations.
2324
2339
Sheng
Zhang
School of Mathematics and Physics
Bohai University
China
szhangchina@126.com
Zhaoyu
Wang
School of Mathematics and Physics
Bohai University
China
1174833500@qq.com
Bilinear form
soliton solution
WKB equations with time-dependent coefficients
Hirota’s bilinear method.
Article.5.pdf
[
[1]
M. J. Ablowitz, P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (1991)
##[2]
M. Arshad, A. R. Seadawy, D.-C. Lu, J. Wang, Travelling wave solutions of Drinfeld-Sokolov-Wilson, Whitham-Broer- Kaup and (2+1)-dimensional Broer-Kaup-Kupershmit equations and their applications, Chin. J. Phys., (2017), -
##[3]
D. Baleanu, B. Agheli, R. Darzi, Analysis of the new technique to solution of fractional wave- and heat-like equation, Acta Phys. Polon. B, 48 (2017), 77-95
##[4]
D. Baleanu, B. Kilic, M. Inc, The first integral method for Wu-Zhang nonlinear system with time-dependent coefficients, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci., 16 (2015), 160-167
##[5]
D. Y. Chen, Introduction of soliton, (Chinese), Science Press, Beijing (2006)
##[6]
S.-H. Chen, P. Grelu, D. Mihalache, F. Baronio, Families of rational solutions of the Kadomtsev-Petviashvili equation, Romanian Rep. Phys., 68 (2016), 1407-1424
##[7]
Y. Chen, Q. Wang, Multiple Riccati equations rational expansion method and complexiton solutions of the Whitham-Broer- Kaup equation, Phys. Lett. A, 347 (2005), 215-227
##[8]
Y. Chen, Q. Wang, B. Li, A generalized method and general form solutions to the Whitham-Broer-Kaup equation, Chaos Solitons Fractals, 22 (2004), 675-682
##[9]
Y. Chen, Q. Wang, B. Li, Elliptic equation rational expansion method and new exact travelling solutions for Whitham- Broer-Kaup equations, Chaos Solitons Fractals, 26 (2005), 231-246
##[10]
D. Y. Chen, X. Y. Zhu, J. B. Zhang, Y. Y. Sun, Y. Shi, New soliton solutions to isospectral AKNS equations, (Chinese) ; translated from Chinese Ann. Math. Ser. A, 33 (2012), 205–216, Chinese J. Contemp. Math., 33 (2012), 167-176
##[11]
S. M. El-Sayed, D. Kaya, Exact and numerical traveling wave solutions of Whitham-Broer-Kaup equations, Appl. Math. Comput., 167 (2005), 1339-1349
##[12]
E.-G. Fan, Travelling wave solutions in terms of special functions for nonlinear coupled evolution systems, Phys. Lett. A, 300 (2002), 243-249
##[13]
C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, Method for solving the Korteweg-deVries equation, Phys. Rev. Lett., 19 (1967), 1095-1097
##[14]
J.-H. He, X.-H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals, 30 (2006), 700-708
##[15]
R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett., 27 (1971), 1192-1194
##[16]
R. Hirota, Exact solution of the modified Korteweg-de Vries equation for multiple collisions of solitons, J. Phys. Soc. Japan, 33 (1972), 1456-1458
##[17]
M. Inc, Constructing solitary pattern solutions of the nonlinear dispersive Zakharov-Kuznetsov equation, Chaos Solitons Fractals, 39 (2009), 109-119
##[18]
M. Inç, On new exact special solutions of the GNLS(m, n, p, q) equations, Modern Phys. Lett. B, 24 (2010), 1769-1783
##[19]
M. Inç, Compact and noncompact structures of a three-dimensional 3DKP(m, n) equation with nonlinear dispersion, Appl. Math. Lett., 26 (2013), 437-444
##[20]
M. Inç, Some special structures for the generalized nonlinear Schrödinger equation with nonlinear dispersion, Waves Random Complex Media, 23 (2013), 77-88
##[21]
M. Inç, E. Ates, Optical soliton solutions for generalized NLSE by using Jacobi elliptic functions, Optoelectron. Adv. Mat., 9 (2015), 1081-1087
##[22]
M. Inç, B. Kilic, D. Baleanu, Optical soliton solutions of the pulse propagation generalized equation in parabolic-law media with space-modulated coefficients, Optik, 127 (2016), 1056-1058
##[23]
M. Inç, Z. S. Korpinar, M. M. Al Qurashi, D. Baleanu, A new method for approximate solutions of some nonlinear equations: residual power series method, Adv. Mech. Eng., 8 (2016), 1-8
##[24]
X.-Y. Jiao, H.-Q. Zhang, An extended method and its application to Whitham-Broer-Kaup equation and two-dimensional perturbed KdV equation, Appl. Math. Comput., 172 (2006), 664-677
##[25]
M. Khalfallah, Exact traveling wave solutions of the Boussinesq-Burgers equation, Math. Comput. Modelling, 49 (2009), 666-671
##[26]
D. Kumar, J. Singh, D. Baleanu, A hybrid computational approach for Klein-Gordon equations on Cantor sets, Nonlinear Dynam., 87 (2017), 511-517
##[27]
G.-D. Lin, Y.-T. Gao, L. Wang, D.-X. Meng, X. Yu, Elastic-inelastic-interaction coexistence and double Wronskian solutions for the Whitham-Broer-Kaup shallow-water-wave model, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3090-3096
##[28]
Y.-B. Liu, A. S. Fokas, D. Mihalache, J.-S. He, Parallel line rogue waves of the third-type Davey-Stewartson equation, Romanian Rep. Phys., 68 (2016), 1425-1446
##[29]
Q. P. Liu, X.-B. Hu, M.-X. Zhang, Supersymmetric modified Korteweg-de Vries equation: bilinear approach, Nonlinearity, 18 (2005), 1597-1603
##[30]
Y. Liu, X.-Q. Liu, Exact solutions of Whitham-Broer-Kaup equations with variable coefficients, Acta Phys. Sin., 63 (2014), 1-9
##[31]
V. B. Matveev, M. A. Salle, Darboux transformations and solitons, Springer Series in Nonlinear Dynamics, Springer- Verlag, Berlin (1991)
##[32]
I. N. McArthur, C. M. Yung, Hirota bilinear form for the super-KdV hierarchy, Modern Phys. Lett. A, 8 (1993), 1739-1745
##[33]
M. R. Miura, Bäcklund transformation, Springer-Verlag, Berlin (1978)
##[34]
A. Mohebbi, Z. Asgari, M. Dehghan, Numerical solution of nonlinear Jaulent-Miodek and Whitham-Broer-Kaup equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 4602-4610
##[35]
S. T. Mohyud-Din, A. Yıldırım, G. Demirli, Traveling wave solutions of Whitham-Broer-Kaup equations by homotopy perturbation method, J. King Saud Univ. Sci., 22 (2010), 173-176
##[36]
M. Rafei, H. Daniali, Application of the variational iteration method to the Whitham-Broer-Kaup equations, Comput. Math. Appl., 54 (2007), 1079-1085
##[37]
V. N. Serkin, A. Hasegawa, Novel soliton solutions of the nonlinear Schrödinger equation model, Phys. Rev. Lett., 85 (2000), 4502-4505
##[38]
V. N. Serkin, A. Hasegawa, T. L. Belyaeva, Nonautonomous solitons in external potentials, Phys. Rev. Lett., 98 (2007), 1-4
##[39]
V. N. Serkin, A. Hasegawa, T. L. Belyaeva, Nonautonomous matter-wave solitons near the Feshbach resonance, Phys. Rev. A, 81 (2010), 1-19
##[40]
J.-W. Shen, W. Xu, Y.-F. Jin, Bifurcation method and traveling wave solution to Whitham-Broer-Kaup equation, Appl. Math. Comput., 171 (2005), 677-702
##[41]
M. Song, J. Cao, X.-L. Guan, Application of the bifurcation method to the Whitham-Broer-Kaup-like equations, Math. Comput. Modelling, 52 (2012), 688-696
##[42]
H. Triki, H. Leblond, D. Mihalache, Soliton solutions of nonlinear diffusion-reaction-type equations with time-dependent coefficients accounting for long-range diffusion, Nonlinear Dynam., 86 (2016), 2115-2126
##[43]
H. Triki, A.-M. Wazwaz, Soliton solutions of the cubic-quintic nonlinear Schrodinger equation with variable coefficients, Romanian J. Phys., 61 (2016), 360-366
##[44]
M.-L. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A, 213 (1996), 279-287
##[45]
A.-M. Wazwaz, The Hirota’s bilinear method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera Kadomtsev-Petviashvili equation, Appl. Math. Comput., 200 (2008), 160-166
##[46]
J. Weiss, M. Tabor, G. Carnevale, The Painlevé property for partial differential equations, J. Math. Phys., 24 (1983), 522-526
##[47]
X.-Y. Wen, A new integrable lattice hierarchy associated with a discrete \(3 \times 3\) matrix spectral problem: N-fold Darboux transformation and explicit solutions, Rep. Math. Phys., 71 (2013), 15-32
##[48]
F.-D. Xie, Z.-Y. Yan, H.-Q. Zhang, Explicit and exact traveling wave solutions of Whitham-Broer-Kaup shallow water equations, Phys. Lett. A, 285 (2001), 76-80
##[49]
G.-Q. Xu, Z.-B. Li, Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations, Chaos Solitons Fractals, 24 (2005), 549-556
##[50]
S.-W. Xu, K. Porsezian, J.-S. He, Y. Cheng, Multi-optical rogue waves of the Maxwell-Bloch equations, Romanian Rep. Phys., 68 (2016), 316-340
##[51]
Z.-L. Yan, X.-Q. Liu, Solitary wave and non-traveling wave solutions to two nonlinear evolution equations, Commun. Theor. Phys. (Beijing), 44 (2005), 479-482
##[52]
Z.-Y. Yan, H.-Q. Zhang, New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water, Phys. Lett. A, 285 (2001), 355-362
##[53]
Z.-L. Yan, J.-P. Zhou, New explicit solutions of (1 + 1)-dimensional variable-coefficient Broer-Kaup system, Commun. Theor. Phys. (Beijing), 54 (2010), 965-970
##[54]
X.-J. Yang, D. Baleanu, H. M. Srivastava, Local fractional integral transforms and their applications, Elsevier/Academic Press, Amsterdam (2015)
##[55]
S. Zhang, Application of Exp-function method to a KdV equation with variable coefficients, Phys. Lett. A, 365 (2007), 448-453
##[56]
S. Zhang, Exact solutions of a KdV equation with variable coefficients via Exp-function method, Nonlinear Dynam., 52 (2008), 11-17
##[57]
P. Zhang, New exact solutions to breaking soliton equations and Whitham-Broer-Kaup equations, Appl. Math. Comput., 217 (2010), 1688-1696
##[58]
S. Zhang, B. Cai, Multi-soliton solutions of a variable-coefficient KdV hierarchy, Nonlinear Dynam., 78 (2014), 1593-1600
##[59]
S. Zhang, M.-T. Chen, Painlevé integrability and new exact solutions of the (4 + 1)-dimensional Fokas equation, Math. Probl. Eng., 2015 (2015), 1-8
##[60]
S. Zhang, M.-T. Chen, W.-Y. Qian, Painlevé analysis for a forced Korteveg-de Vries equation arisen in fluid dynamics of internal solitary waves, Therm. Sci., 19 (2015), 1223-1226
##[61]
S. Zhang, X.-D. Gao, Mixed spectral AKNS hierarchy from linear isospectral problem and its exact solutions, Open Phys., 13 (2015), 310-322
##[62]
S. Zhang, X.-D. Gao, Exact N-soliton solutions and dynamics of a new AKNS equation with time-dependent coefficients, Nonlinear Dynam., 83 (2016), 1043-1052
##[63]
S. Zhang, D. Liu, Multisoliton solutions of a (2 + 1)-dimensional variable-coefficient Toda lattice equation via Hirota’s bilinear method, Canad. J. Phys., 92 (2014), 184-190
##[64]
S. Zhang, D.-D. Liu, The third kind of Darboux transformation and multisoliton solutions for generalized Broer-Kaup equations, Turkish J. Phys., 39 (2015), 165-177
##[65]
S. Zhang, C. Tian, W.-Y. Qian, Bilinearization and new multisoliton solutions for the (4 + 1)-dimensional Fokas equation, Pramana, 86 (2016), 1259-1267
##[66]
S. Zhang, D. Wang, Variable-coefficient nonisospectral Toda lattice hierarchy and its exact solutions, Pramana, 85 (2015), 1143-1156
##[67]
S. Zhang, T.-C. Xia, A generalized F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equations, Appl. Math. Comput., 183 (2006), 1190-1200
##[68]
S. Zhang, T.-C. Xia, A generalized auxiliary equation method and its application to (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations, J. Phys. A, 40 (2007), 227-248
##[69]
S. Zhang, B. Xu, H.-Q. Zhang, Exact solutions of a KdV equation hierarchy with variable coefficients, Int. J. Comput. Math., 91 (2014), 1601-1616
##[70]
S. Zhang, H.-Q. Zhang, An Exp-function method for a new N-soliton solutions with arbitrary functions of a (2 + 1)- dimensional vcBK system, Comput. Math. Appl., 61 (2011), 1923-1930
##[71]
S. Zhang, H.-Q. Zhang, Fractional sub-equation method and its applications to nonlinear fractional PDEs, Phys. Lett. A, 375 (2011), 1069-1073
##[72]
S. Zhang, L.-Y. Zhang, Bilinearization and new multi-soliton solutions of mKdV hierarchy with time-dependent coefficients, Open Phys., 14 (2016), 69-75
]
On some subclasses of hypergeometric functions with Djrbashian Cauchy type kernel
On some subclasses of hypergeometric functions with Djrbashian Cauchy type kernel
en
en
In this paper, some new integral representations are proved for several weighted hypergeometric functions introduced
recently in [J. E. Restrepo, A. Kılıc¸man, P. Agarwal, O. Altun, Adv. Difference Equ., 2017 (2017), 11 pages]. Besides, some new
subclasses of weighted hypergeometric functions containing the Djrbashian Cauchy type kernel are introduced. The series representing
the considered hypergeometric functions are convergent out of some sets of zero !-capacity, and these hypergeometric
functions have finite boundary values everywhere on \(|z|=1\), out of zero \(\omega\)-capacity sets.
2340
2349
Joel Esteban
Restrepo
Institute of Mathematics
University of Antioquia
Colombia
cocojoel89@yahoo.es
Armen
Jerbashian
Institute of Mathematics
University of Antioquia
Colombia
armen-jerbashian@yahoo.com
Praveen
Agarwal
Department of Mathematics
Anand International College of Engineering
India
goyal.praveen2011@gmail.com
Weighted hypergeometric function
Djrbashian Cauchy type kernel
\(\omega\)-capacity
boundary behavior.
Article.6.pdf
[
[1]
P. Agarwal, J.-S. Choi, K. B. Kachhia, J. C. Prajapati, H. Zhou, Some integral transforms and fractional integral formulas for the extended hypergeometric functions, Commun. Korean Math. Soc., 31 (2016), 591-601
##[2]
W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics, Stechert-Hafner, Inc., New York (1964)
##[3]
M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math., 78 (1997), 19-32
##[4]
M. A. Chaudhry, A. Qadir, H. M. Srivastava, R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput., 159 (2004), 589-602
##[5]
A. M. Dzhrbashyan, An extension of the factorization theory of M. M. Dzhrbashyan, (Russian); translated from Izv. Nats. Akad. Nauk Armenii Mat., 30 (1995), 47–75, J. Contemp. Math. Anal., 30 (1995), 39-61
##[6]
M. M. Dzhrbashyan, V. S. Zakharyan, Klassy i granichnye svoĭstva funktsiĭ, meromorfnykh v kruge, (Russian) [[Classes and boundary properties of functions that are meromorphic in the disk]] Fizmatlit “Nauka”, Moscow (1993)
##[7]
M. M. Džrbašjan, Theory of factorization and boundary properties of functions meromorphic in the disk, Proceedings of the International Congress of Mathematician, Vancouver, B. C., (1974), Canad. Math. Congress, Montreal, Que., 2 (1975), 197-202
##[8]
O. Frostman, Potentiel d’équilibre et capacité des ensembles avec quelques applications a la théorie des fonctions, (French) Madd. Lunds. Univ. Mat. Sem., 3 (1935), 1-11
##[9]
O. Frostman, Sur les produits de Blaschke, Fysiogr. Säldsk. Lund, föhr., 12 (1939), 1-14
##[10]
O. Frostman, Sur les produits de Blaschke, (French) Kungl. Fysiografiska S¨allskapets i Lund Förhandlingar [Proc. Roy. Physiog. Soc. Lund], 12 (1942), 169-182
##[11]
I. O. Kiymaz, A. Çetinkaya, P. Agarwal, An extension of Caputo fractional derivative operator and its applications, J. Nonlinear Sci. Appl., 9 (2016), 3611-3621
##[12]
L. K. B. Kuroda, A. V. Gomes, R. Tavoni, P. F. de Arruda Mancera, N. Varalta, R. de Figueiredo Camargo, Unexpected behavior of Caputo fractional derivative, Comput. Appl. Math., 36 (2017), 1173-1183
##[13]
E. Özergin, Some properties of hypergeometric functions, Ph.D. Thesis, Eastern Mediterranean University, North Cyprus, Turkey (2011)
##[14]
J. E. Restrepo, A. Kılıçman, P. Agarwal, O. Altun, Weighted hypergeometric functions and fractional derivative, Adv. Difference Equ., 2017 (2017), 1-11
##[15]
V. E. Tarasov, Some identities with generalized hypergeometric functions, Appl. Math. Inf. Sci., 10 (2016), 1729-1734
##[16]
X.-J. Yang, D. Baleanu, H. M. Srivastava, Local fractional integral transforms and their applications, Elsevier/Academic Press, Amsterdam (2016)
##[17]
X.-J. Yang, H. M. Srivastava, An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives, Commun. Nonlinear Sci. Numer. Simul., 29 (2015), 499-504
]
Fixed point results for generalized \(\Theta\)-contractions
Fixed point results for generalized \(\Theta\)-contractions
en
en
The aim of this paper is to extend the result of [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages] by applying
a simple condition on the function \(\Theta\). With this condition, we also prove some fixed point theorems for Suzuki-Berinde type
\(\Theta\)-contractions which generalize various results of literature. Finally, we give one example to illustrate the main results in this
paper.
2350
2358
Jamshaid
Ahmad
Department of Mathematics
University of Jeddah
Saudi Arabia
jamshaid_jasim@yahoo.com
Abdullah E.
Al-Mazrooei
Department of Mathematics
University of Jeddah
Saudi Arabia
aealmazrooei@uj.edu.sa
Yeol Je
Cho
Department of Mathematics Education and the RINS
Center for General Education
Gyeongsang National University
China Medical University
Korea
Taiwan
yjcho@gnu.ac.kr
Young-Oh
Yang
Department of Mathematics
Jeju National University
Korea
yangyo@jejunu.ac.kr
Complete metric space
\(\Theta\)-contraction
Suzuki-Berinde type \(\Theta\)-contraction
fixed point.
Article.7.pdf
[
[1]
A. Ahmad, A. S. Al-Rawashdeh, A. Azam, Fixed point results for \(\{\alpha,\xi\}\)-expansive locally contractive mappings, J. Inequal. Appl., 2014 (2014), 1-10
##[2]
J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized F-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-18
##[3]
A. Al-Rawashdeh, J. Ahmad, Common fixed point theorems for JS-contractions, Bull. Math. Anal. Appl., 8 (2016), 12-22
##[4]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[5]
V. Berinde, General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces, Carpathian J. Math., 24 (2008), 10-19
##[6]
L. B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273
##[7]
M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74-79
##[8]
N. Hussain, V. Parvaneh, B. Samet, C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-17
##[9]
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
##[10]
Z.-L. Li, S.-J. Jiang, Fixed point theorems of JS-quasi-contractions, Fixed Point Theory Appl., 2016 (2016), 1-11
##[11]
T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317
##[12]
F. Vetro, A generalization of Nadler fixed point theorem, Carpathian J. Math., 31 (2015), 403-410
]
Fixed point results for generalized contractive multivalued maps
Fixed point results for generalized contractive multivalued maps
en
en
In this paper, we prove some results on the existence of fixed points for multivalued maps with respect to general distance.
Our results improve and generalize a number of known fixed point results including the fixed point results.
2359
2365
Aljazi M.
Alkhammash
Department of Mathematics
King Abdulaziz University
Saudi Arabia
AAlkhamash@hotmail.com
Afrah A. N.
Abdou
Department of Mathematics
King Abdulaziz University
Saudi Arabia
aabdou@kau.edu.sa
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Metric space
fixed point
w-distance
multivalued contractive map
Banach limit.
Article.8.pdf
[
[1]
C.-S. Chuang, L.-J. Lin, W. Takahashi, Fixed point theorems for single-valued and set-valued mappings on complete metric spaces, J. Nonlinear Convex Anal., 13 (2012), 515-527
##[2]
Y.-Q. Feng, S.-Y. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl., 317 (2006), 103-112
##[3]
K. Hasegawa, T. Komiya, W. Takahashi, Fixed point theorems for general contractive mappings in metric spaces and estimating expressions, Sci. Math. Jpn., 74 (2011), 15-27
##[4]
T. Husain, A. Latif, Fixed points of multivalued nonexpansive maps, Internat. J. Math. Math. Sci., 14 (1991), 421-430
##[5]
O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44 (1996), 381-391
##[6]
M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69 (2008), 2942-2949
##[7]
D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139
##[8]
A. Latif, A. A. N. Abdou, Fixed points of generalized contractive maps, Fixed Point Theory Appl., 2009 (2009), 1-9
##[9]
A. Latif, A. A. N. Abdou, Multivalued generalized nonlinear contractive maps and fixed points, Nonlinear Anal., 74 (2011), 1436-1444
##[10]
A. Latif, W. A. Albar, Fixed point results in complete metric spaces, Demonstratio Math., 41 (2008), 145-150
##[11]
L.-J. Lin, T. Z. Yu, G. Kassay, Existence of equilibria for multivalued mappings and its application to vectorial equilibria, J. Optim. Theory Appl., 114 (2002), 189-208
##[12]
N. B. Minh, N. X. Tan, Some sufficient conditions for the existence of equilibrium points concerning multivalued mappings, Vietnam J. Math., 28 (2000), 295-310
##[13]
S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
##[14]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488-502
##[15]
S. Shukla, Set-valued generalized contractions in 0-complete partial metric spaces, J. Nonlinear Funct. Anal., 2014 (2014), 1-20
##[16]
T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869
##[17]
T. Suzuki, W. Takahashi, Fixed point theorems and characterizations of metric completeness, Topol. Methods Nonlinear Anal., 8 (1996), 371-382
##[18]
W. Takahashi, Existence theorems generalizing fixed point theorems for multivalued mappings, Fixed point theory and applications, Marseille, (1989), Pitman Res. Notes Math. Ser., Longman Sci. Tech., Harlow, 252 (1991), 397-406
##[19]
W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
##[20]
W. Takahashi, N.-C. Wong, J.-C. Yao, Fixed point theorems for general contractive mappings with W-distances in metric spaces, J. Nonlinear Convex Anal., 14 (2013), 637-648
##[21]
F.-H. Zhao, L. Yang, Hybrid projection methods for equilibrium problems and fixed point problems of infinite family of multivalued asymptotically nonexpansive mappings, J. Nonlinear Funct. Anal., 2016 (2016), 1-13
]
Solvability of fractional p-Laplacian boundary value problems with controlled parameters
Solvability of fractional p-Laplacian boundary value problems with controlled parameters
en
en
This paper aims to investigate existence of solutions of several boundary value problems for fractional one-dimensional
p-Laplacian equation under controlled parameters. By employing fixed point theory and critical point theory, some new results
are obtained, which enrich and generalize the previous results.
2366
2383
Tengfei
Shen
School of Mathematics
China University of Mining and Technology
P. R. China
stfcool@126.com
Wenbin
Liu
School of Mathematics
China University of Mining and Technology
P. R. China
cumt_equations@126.com
Fractional ordinary differential equation
boundary value problem
p-Laplacian operator
existence.
Article.9.pdf
[
[1]
R. P. Agarwal, D. O’Regan, S. Staněk, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J. Math. Anal. Appl., 371 (2010), 57-68
##[2]
R. P. Agarwal, Y. Zhou, Y.-Y. He, Existence of fractional neutral functional differential equations, Comput. Math. Appl., 59 (2010), 1095-1100
##[3]
C.-Z. Bai, Existence of positive solutions for boundary value problems of fractional functional differential equations , Electron. J. Qual. Theory Differ. Equ., 2010 (2010), 1-14
##[4]
M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008), 1340-1350
##[5]
M. Bergounioux, A. Leaci, G. Nardi, F. Tomarelli, Fractional Sobolev spaces and functions of bounded variation, ArXiv, 2016 (2016), 1-19
##[6]
G. Bonanno, G. Riccobono, Multiplicity results for Sturm-Liouville boundary value problems, Appl. Math. Comput., 210 (2009), 294-297
##[7]
G. Bonanno, R. Rodríguez-López, S. Tersian, Existence of solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 717-744
##[8]
D. Bonheure, P. Habets, F. Obersnel, P. Omari, Classical and non-classical solutions of a prescribed curvature equation, J. Differential Equations, 243 (2007), 208-237
##[9]
G. Cerami, An existence criterion for the critical points on unbounded manifolds, (Italian) Istit. Lombardo Accad. Sci. Lett. Rend. A, 112 (1978), 332-336
##[10]
T.-Y. Chen, W.-B. Liu, Solvability of fractional boundary value problem with p-Laplacian via critical point theory, Bound. Value Probl., 2016 (2016), 1-12
##[11]
B. Du, X.-P. Hu, W.-G. Ge, Positive solutions to a type of multi-point boundary value problem with delay and onedimensional p-Laplacian, Appl. Math. Comput., 208 (2009), 501-510
##[12]
I. Ekeland, Convexity methods in Hamiltonian mechanics, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], Springer-Verlag, Berlin (1990)
##[13]
M. Fečkan, Y. Zhou, J.-R. Wang, On the concept and existence of solution for impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 3050-3060
##[14]
D. J. Guo, V. Lakshmikantham, Nonlinear problems in abstract cones, Notes and Reports in Mathematics in Science and Engineering, Academic Press, Inc., Boston, MA (1988)
##[15]
D. Idczak, S. Walczak, Fractional Sobolev spaces via Riemann-Liouville derivatives, J. Funct. Spaces Appl., 2013 (2013), 1-15
##[16]
W.-H. Jiang, The existence of solutions to boundary value problems of fractional differential equations at resonance, Nonlinear Anal., 74 (2011), 1987-1994
##[17]
F. Jiao, Y. Zhou, Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl., 62 (2011), 1181-1199
##[18]
F. Jiao, Y. Zhou, Existence results for fractional boundary value problem via critical point theory, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 22 (2012), 1-17
##[19]
H. Jin, W.-B. Liu, Eigenvalue problem for fractional differential operator containing left and right fractional derivatives, Adv. Difference Equ., 2016 (2016), 1-12
##[20]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[21]
N. Kosmatov, A boundary value problem of fractional order at resonance, Electron. J. Differential Equations, 2010 (2010), 1-10
##[22]
V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal., 69 (2008), 3337-3343
##[23]
K. Q. Lan, W. Lin, Positive solutions of systems of Caputo fractional differential equations, Commun. Appl. Anal., 17 (2013), 61-85
##[24]
J. Leszczynski, T. Blaszczyk, Modeling the transition between stable and unstable operation while emptying a silo, Granul. Matter, 13 (2011), 429-438
##[25]
Y.-J. Liu, W.-G. Ge, Multiple positive solutions to a three-point boundary value problem with p-Laplacian, J. Math. Anal. Appl., 277 (2003), 293-302
##[26]
F. Mainardi, Fractional diffusive waves in viscoelastic solids, J. L. Wegner, F. R. Norwood (Eds.), IUTAM Symposium– Nonlinear Waves in Solids, ASME/AMR, Fairfield, NJ, (1995), 93-97
##[27]
J. Mawhin, Some boundary value problems for Hartman-type perturbations of the ordinary vector p-Laplacian, Lakshmikantham’s legacy: a tribute on his 75th birthday, Nonlinear Anal., 40 (2000), 497-503
##[28]
J. Mawhin, M. Willem, Critical point theory and Hamiltonian systems, Applied Mathematical Sciences, Springer- Verlag, New York (1989)
##[29]
M. L. Morgado, N. J. Ford, P. M. Lima, Analysis and numerical methods for fractional differential equations with delay, J. Comput. Appl. Math., 252 (2013), 159-168
##[30]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[31]
P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (1986)
##[32]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Theory and applications, Edited and with a foreword by S. M. Nikolski˘ı, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon (1993)
##[33]
T.-F. Shen,W.-B. Liu, X.-H. Shen, Existence and uniqueness of solutions for several BVPs of fractional differential equations with p-Laplacian operator, Mediterr. J. Math., 13 (2016), 4623-4637
##[34]
J. Simon, Régularité de la solution d’un probléme aux limites non linéaires, (French) [[Regularity of the solution of a nonlinear boundary problem]] Ann. Fac. Sci. Toulouse Math., 3 (1981), 247-274
##[35]
E. Szymanek, The application of fractional order differential calculus for the description of temperature profiles in a granular layer, Adv. Theory Appl. Non-integer Order Syst., Springer Inter. Publ., Switzerland (2013)
##[36]
X. H. Tang, L. Xiao, Homoclinic solutions for ordinary p-Laplacian systems with a coercive potential, Nonlinear Anal., 71 (2009), 1124-1132
##[37]
Y. Tian, W.-G. Ge, Second-order Sturm-Liouville boundary value problem involving the one-dimensional p-Laplacian, Rocky Mountain J. Math., 38 (2008), 309-327
##[38]
C. Torres, Mountain pass solution for a fractional boundary value problem, J. Fract. Calc. Appl., 5 (2014), 1-10
##[39]
Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear Anal., 71 (2009), 3249-3256
]
Fourier series of sums of products of poly-Bernoulli functions and their applications
Fourier series of sums of products of poly-Bernoulli functions and their applications
en
en
In this paper, we consider three types of sums of products of poly-Bernoulli functions and derive Fourier series expansions
of them. In addition, we express those three types of functions in terms of Bernoulli functions.
2384
2401
Taekyun
Kim
Department of Mathematics
Kwangwoon University
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Dmitry V.
Dolgy
Hanrimwon
Kwangwoon University
Republic of Korea
dvdolgy@gmail.com
Jin-Woo
Park
Department of Mathematics Education
Daegu University
Republic of Korea
a0417001@knu.ac.kr
Fourier series
Bernoulli polynomial
poly-Bernoulli polynomial
poly-Bernoulli function.
Article.10.pdf
[
[1]
T. Arakawa, M. Kaneko, On poly-Bernoulli numbers, Comment. Math. Univ. St. Paul., 48 (1999), 159-167
##[2]
A. Bayad, Y. Hamahata, Multiple polylogarithms and multi-poly-Bernoulli polynomials, Funct. Approx. Comment. Math., 46 (2012), 45-61
##[3]
D. V. Dolgy, D. S. Kim, T. Kim, T. Mansour, Degenerate poly-Bernoulli polynomials of the second kind, J. Comput. Anal. Appl., 21 (2016), 954-966
##[4]
G. V. Dunne, C. Schubert, Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys., 7 (2013), 225-249
##[5]
C. Faber, R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math., 139 (2000), 173-199
##[6]
I. M. Gessel, On Miki’s identity for Bernoulli numbers, J. Number Theory, 110 (2005), 75-82
##[7]
M. Kaneko, Poly-Bernoulli numbers, J. Théor. Nombres Bordeaux, 9 (1997), 221-228
##[8]
D. S. Kim, D. V. Dolgy, T. Kim, S.-H. Rim, Some formulae for the product of two Bernoulli and Euler polynomials, Abstr. Appl. Anal., 2012 (2012), 1-15
##[9]
D. S. Kim, T. Kim, Bernoulli basis and the product of several Bernoulli polynomials, Int. J. Math. Math. Sci., 2012 (2012), 1-12
##[10]
D. S. Kim, T. Kim, Some identities of higher order Euler polynomials arising from Euler basis, Integral Transforms Spec. Funct., 24 (2013), 734-738
##[11]
D. S. Kim, T. Kim, A note on degenerate poly-Bernoulli numbers and polynomials, Adv. Difference Equ., 2015 (2015), 1-8
##[12]
D. S. Kim, T. Kim, A note on poly-Bernoulli and higher-order poly-Bernoulli polynomials, Russ. J. Math. Phys., 22 (2015), 26-33
##[13]
D. S. Kim, T. Kim, Higher-order Bernoulli and poly-Bernoulli mixed type polynomials, Georgian Math. J., 22 (2015), 265-272
##[14]
D. S. Kim, T. Kim, H. I. Kwon, T. Mansour, Degenerate poly-Bernoulli polynomials with umbral calculus viewpoint, J. Inequal. Appl., 2015 (2015), 1-13
##[15]
D. S. Kim, T. Kim, T. Mansour, J.-J. Seo, Fully degenerate poly-Bernoulli polynomials with a q parameter, Filomat, 30 (2016), 1029-1035
##[16]
T. Kim, D. S. Kim, S.-H. Rim, D. V. Dolgy, Fourier series of higher-order Bernoulli functions and their applications, J. Inequal. Appl., 2017 (2017), 1-7
##[17]
T. Kim, D. S. Kim, J.-J. Seo, Fully degenerate poly-Bernoulli numbers and polynomials, Open Math., 14 (2016), 545-556
##[18]
J. E. Marsden, Elementary classical analysis, With the assistance of Michael Buchner, Amy Erickson, Adam Hausknecht, Dennis Heifetz, Janet Macrae and William Wilson, and with contributions by Paul Chernoff, Istv´an F´ary and Robert Gulliver, W. H. Freeman and Co., San Francisco, (1974), -
##[19]
K. Shiratani, S. Yokoyama, An application of p-adic convolutions, Mem. Fac. Sci. Kyushu Univ. Ser. A, 36 (1982), 73-83
##[20]
P. T. Young, Bernoulli and poly-Bernoulli polynomial convolutions and identities of p-adic Arakawa-Kaneko zeta functions, J. Number Theory, 12 (2016), 1295-1309
##[21]
D. G. Zill, M. R. Cullen, Advanced engineering mathematics, second edition, Jones & Bartlett Learning, Massachusetts (2000)
]
Application of fixed point theory for approximating of a positive-additive functional equation in intuitionistic random C*-algebras
Application of fixed point theory for approximating of a positive-additive functional equation in intuitionistic random C*-algebras
en
en
We apply a fixed point theorem for approximating of a positive-additive functional equation in intuitionistic random \(C^*\)-
algebras.
2402
2407
Javad
Vahidi
Department of Mathematics
Iran University of Science and Technology
Iran
jvahidi@iust.ac.ir
Approximation
fixed point theory
intuitionistic
random normed spaces
\(C^*\)- algebra.
Article.11.pdf
[
[1]
A. A. N. Abdou, Y. J. Cho, R. Saadati, Distribution and survival functions with applications in intuitionistic random Lie \(C^*\)-algebras, J. Comput. Anal. Appl., 21 (2016), 345-354
##[2]
L. Cădariu, V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber., 346 (2004), 43-52
##[3]
L. Cădariu, V. Radu, Fixed point methods for the generalized stability of functional equations in a single variable, Fixed Point Theory and Appl., 2008 (2008), 1-15
##[4]
Y. J. Cho, Th. M. Rassias, R. Saadati, Stability of functional equations in random normed spaces, Springer Optimization and Its Applications, Springer, New York (2013)
##[5]
Y. J. Cho, R. Saadati, Lattictic non-Archimedean random stability of ACQ functional equation, Adv. Difference Equ., 2011 (2011), 1-12
##[6]
J. Diaz, B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305-309
##[7]
J. Dixmier, \(C^*\)-Algebras, North-Holland Publ. Com., Amsterdam, New York and Oxford (1977)
##[8]
K. R. Goodearl, Notes on Real and Complex \(C^*\)-Algebras, Shiva Math. Series IV, Shiva Publ. Limited, England (1982)
##[9]
J. I. Kang, R. Saadati, Approximation of homomorphisms and derivations on non-Archimedean random Lie \(C^*\)-algebras via fixed point method, J. Inequal. Appl., 2012 (2012), 1-10
##[10]
S. J. Lee, R. Saadati, On stability of functional inequalities at random lattice \(\phi\)-normed spaces, J. Comput. Anal. Appl., 15 (2013), 1403-1412
##[11]
D. Miheţ, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343 (2008), 567-572
##[12]
D. Miheţ, R. Saadati, On the stability of the additive Cauchy functional equation in random normed spaces, Appl. Math. Lett., 24 (2011), 2005-2009
##[13]
D. Miheţ, R. Saadati, S. M. Vaezpour, The stability of the quartic functional equation in random normed spaces, Acta Appl. Math., 110 (2010), 797-803
##[14]
M. Mohamadi, Y. J. Cho, C. Park, P. Vetro, R. Saadati, Random stability on an additive-quadratic-quartic functional equation, J. Inequal. Appl., 2010 (2010), 1-18
##[15]
C. Park, M. Eshaghi Gordji, R. Saadati, Random homomorphisms and random derivations in random normed algebras via fixed point method, J. Inequal. Appl., 2012 (2012), 1-13
##[16]
C. Park, H. A. Kenary, S. Og Kim, Positive-additive functional equations in \(C^*\)-algebras, Fixed Point Theory, 13 (2012), 613-622
##[17]
J. M. Rassias, R. Saadati, Gh. Sadeghi, J. Vahidi, On nonlinear stability in various random normed spaces, J. Inequal. Appl., 2011 (2011), 1-17
##[18]
R. Saadati, Th. M. Rassias, Y. J. Cho, Z. H. Wang, Distribution and survival functions and application in intuitionistic random approximation, Appl. Math. Inf. Sci., 9 (2015), 2535-2540
##[19]
R. Saadati, S. M. Vaezpour, Y. J. Cho, A note to paper ”On the stability of cubic mappings and quartic mappings in random normed spaces” , J. Inequal. Appl., 2009 (2009), 1-6
##[20]
J. Vahidi, C. Park, R. Saadati , A functional equation related to inner product spaces in non-Archimedean L-random normed spaces, J. Inequal. Appl., 2012 (2012), 1-16
]
A linear multisensor PHD filters via the measurement product space
A linear multisensor PHD filters via the measurement product space
en
en
The probability hypothesis density (PHD) is the first moment of RFS. Its integral over any region gives the expectation
number of targets in that region. In the finite set statistics (FISST) framework, the PHD recursion, or PHD filter, approximate
the multi-target Bayes recursion. This paper deals with the multisensor PHD filter under a linear correlation condition through
multisensor product space and the measurement dimension extension (MDE) approach, which remains the similar appearance
like the conventional PHD filters except the product space and some parameters in the filters. However, in the product space
the dimension extended measurements may greatly increase the computational load. Therefore, we propose a fast algorithm
for the linear multisensor PHD (LM-PHD) filters to increase the running speed and with cost of slightly sacrificing the tracking
performance.
2408
2422
Weifeng
Liu
School of Automation
Science and Technology on Electro-optic Control Laboratory
Hangzhou Dianzi University
P. R. China
P. R. China
dashan_liu@hdu.edu.cn
Yimei
Chen
School of Automation
Hangzhou Dianzi University
P. R. China
chenyimei245600@163.com
Chenglin
Wen
School of Automation
Hangzhou Dianzi University
P. R. China
wencl@hdu.edu.cn
Hailong
Cui
School of Automation
Hangzhou Dianzi University
P. R. China
16528585@qq.com
Linear correlation
random finite set
PHD filter
dimension extension of measurements
product space.
Article.12.pdf
[
[1]
Y. Bar-Shalom, Tracking methods in a multitarget environment, IEEE Trans. Autom. Control, 23 (1978), 618-626
##[2]
K. Chang, M. E. Pollock, M. K. Skrehot, Space-based millimeter wave debris tracking radar, Proc. SPIE, Monolithic Microwave Integrated Circuits for Sensors, Radar, and Communications Systems, Orlando, FL, 1475 (1991), 257-266
##[3]
L. Chen, Z.-Y. Zhao, H. Yan, A Probabilistic Relaxation Labeling (PRL) based method for C. elegans cell tracking in microscopic image sequences, IEEE J. Sel. Topics Signal Process, 10 (2016), 185-192
##[4]
H. Deusch, S. Reuter, K. Dietmayer, The labeled multi-Bernoulli SLAM filter, IEEE Trans. Signal Process., 22 (2015), 1561-1565
##[5]
W. J. Farrell, Interacting multiple model filter for tactical ballistic missile tracking, IEEE Trans. Aerosp. Electron. Syst., 44 (2008), 418-426
##[6]
C. Huang, Y. Li, R. Nevatia, Multiple target tracking by learning-based hierarchical association of detection responses, IEEE Trans. Pattern Anal. Mach. Intell., 35 (2013), 898-910
##[7]
J.-W. Kim, P. Menon, E. Ohlmeyer, Motion models for use with the Maneuvering Ballistic Missile tracking estimators, Proceedings of the AIAA guidance, navigation, and control conference, Toronto, Ontario, Canada, (2010), 1-13
##[8]
M. F. Kircher, S. S. Gambhir, J. Grimm, Noninvasive cell-tracking methods, Nat. Rev. Clin. Oncol., 8 (2011), 677-688
##[9]
F. Lian, C.-Z. Han, W.-F. Liu, H. Chen, Joint spatial registration and multi-target tracking using an extended probability hypothesis density filter, IET radar, sonar & navigation, 5 (2011), 441-448
##[10]
L. Lin, Y. Bar-Shalom, T. Kirubarajan, Track labeling and PHD filter for multitarget tracking, IEEE Trans. Aerosp. Electron. Syst., 42 (2006), 778-795
##[11]
W.-F. Liu, C.-L. Wen, A linear multisensor PHD filter using the measurement dimension extension approach, Advances in Swarm Intelligence: the 2th International Conference on Swarm Intelligence, Chongqing, China, (2011), 486-493
##[12]
W.-F. Liu , C.-L.Wen, The fast linear multisensor RFS-multitarget tracking filters, Proceedings of the 17th International Conference on Information Fusion, Slamanca, Spanish, (2014), 1-8
##[13]
R. P. S. Mahler, Multitarget Bayes filtering via first-order multitarget moments, IEEE Trans. Aerosp. Electron. Syst, 39 (2003), 1152-1178
##[14]
R. P. S. Mahler, PHD filters of higher order in target number, IEEE Trans. Aerosp. Electron. Syst., 43 (2007), 1523-1543
##[15]
R. P. S. Mahler, Statistical multisource-multitarget information fusion, Artech House, Inc., Norwood, MA, USA (2007)
##[16]
R. P. S. Mahler, Approximate multisensor CPHD and PHD filters, Proceedings of the 13th International Conference on Information Fusion, (2010), 1152-1178
##[17]
R. P. S. Mahler, Advances in statistical multisource-multitarget information fusion, Artech House, Inc., Norwood, MA, USA (2014)
##[18]
R. P. S. Mahler, B.-T. Vo, B.-N. Vo, Forward-backward probability hypothesis density smoothing, IEEE Trans. Aerosp. Electron. Syst., 48 (2012), 707-728
##[19]
N. Nandakumaran, K. Punithakumar, T. Kirubarajan, Improved multi-target tracking using probability hypothesis density smoothing, Proceedings of the SPIE Conference on Signal and Processing of Small Targets, 6699 (2007), 1-6
##[20]
K. Panta, B.-N. Vo, S. Singh, Novel data association schemes for the probability hypothesis density filter, IEEE Trans. Aerosp. Electron. Syst., 43 (2007), 556-570
##[21]
J. N. Pelton, Tracking of orbital debris and avoidance of satellite collisions, Handbook of Satellite Applications, Springer, New York, (2016), 1-13
##[22]
D. B. Reid, An algorithm for tracking multiple targets, IEEE Trans. Autom. Control, 24 (1979), 843-854
##[23]
S. Reuter, B.-T. Vo, B.-N. Vo, K. Dietmayer, The labeled multi-Bernoulli filter, IEEE Trans. Signal Process., 62 (2014), 3246-3260
##[24]
B. G. Saulson, K.-C. Chang, Nonlinear estimation comparison for ballistic missile tracking, Opt. Eng., 43 (2004), 1424-1438
##[25]
D. Schuhmacher, B.-T. Vo, B.-N. Vo, A consistent metric for performance evaluation of multi-object filters, IEEE Trans. Signal Process., 56 (2008), 3447-3457
##[26]
H. Sidenbladh, Multi-target particle filtering for the probability hypothesis density, ArXiv, 2003 (2003), 1-7
##[27]
R. Suwantong, Development of the Moving HorizonEstimator with Pre-Estimation (MHE-PE), Application to Space Debris Tracking during the Re-Entries, Automatic, Supélec (2014)
##[28]
B.-N. Vo, W.-K. Ma, The Gaussian mixture probability hypothesis density filter, IEEE Trans. Signal Process., 54 (2006), 4091-4104
##[29]
B.-N. Vo, S. Singh, A. Doucet, Sequential Monte Carlo implementation of the PHD filter for multi-target tracking, PProceedings of the International Conference on Information Fusion, Cairns, Australia, (2003), 792-799
##[30]
B.-T. Vo, B.-N. Vo, Labeled random finite sets and multi-object conjugate priors, IEEE Trans. Signal Process., 13 (2013), 3460-3475
##[31]
B.-T. Vo, B.-N. Vo, A. Cantoni, Analytic implementations of the cardinalized probability hypothesis density filter, IEEE Trans. Signal Process., 55 (2007), 3553-3567
##[32]
B.-T. Vo, B.-N. Vo, A. Cantoni, The cardinality balanced multi-target multi-Bernoulli filter and its implementations, IEEE Trans. Signal Process., 57 (2009), 409-423
##[33]
B.-N. Vo, B.-T. Vo, R. P. S. Mahler, Closed-form solutions to forwardbackward smoothing, IEEE Trans. Signal Process., 60 (2012), 2-17
##[34]
B.-N. Vo, B.-T. Vo, D. Phung, Labeled random finite sets and the Bayes multi-target tracking filter, IEEE Trans. Signal Process., 62 (2014), 6554-6567
##[35]
Q. Yu, G. Medioni, Multiple-target tracking by spatiotemporal monte carlo markov chain data association, IEEE Trans. Pattern Anal. Mach. Intell., 31 (2009), 2196-2210
##[36]
T. Zajic, R. Mahler, Particle-systems implementation of the PHD multitarget-tracking filter, Proc. SPIE, Signal Processing, Sensor Fusion, and Target Recognition XII, 5096 (2003), 291-299
]
Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method
Approximate solutions of fuzzy differential equations of fractional order using modified reproducing kernel Hilbert space method
en
en
In this paper, we use the modified reproducing kernel Hilbert space method to approximate the solution of fuzzy differential
equations of fractional order. Using this method, we construct a new algorithm to approximate the solution of such differential
equations. The proposed algorithm produces solutions in terms of interval-valued fuzzy numbers. Two numerical examples
are tested and the results showed that the proposed algorithm is able to produce solutions that approach to the exact solutions.
It concludes that the proposed algorithm can be considered as a modern algorithm that complements to the existing ones.
2423
2439
Asia Khalaf
Albzeirat
Institute of Engineering Mathematics
Universiti Malaysia Perlis
Malaysia
asiajor@yahoo.com
Muhammad Zaini
Ahmad
Institute of Engineering Mathematics
Universiti Malaysia Perlis
Malaysia
Shaher
Momani
Department of Mathematics, Faculty of Science
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science
The University of Jordan
King Abdulaziz University
Jordan
Saudi Arabia
Norazrizal Aswad Abdul
Rahman
Institute of Engineering Mathematics
Universiti Malaysia Perlis
Malaysia
Caputo fractional derivative
fuzzy differential equation of fractional order
modified reproducing kernel Hilbert space method.
Article.13.pdf
[
[1]
O. Abu Arqub, An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations, J. Comput. Anal. Appl., 8 (2015), 857-874
##[2]
O. Abu Arqub, M. Al-Smadi, S. Momani, Application of reproducing kernel method for solving nonlinear Fredholm- Volterra integrodifferential equations, Abstr. Appl. Anal., 2012 (2012), 1-16
##[3]
R. P. Agarwal, V. Lakshmikantham, J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72 (2010), 2859-2862
##[4]
M. Z. Ahmad, M. K. Hasan, S. Abbasbandy, Solving fuzzy fractional differential equations using Zadeh’s extension principle, Scientific World J., 2013 (2013), 1-11
##[5]
A. Ahmadian, S. Salahshour, C. S. Chan, A Runge–Kutta method with reduced number of function evaluations to solve hybrid fuzzy differential equations, Soft Comput., 19 (2015), 1051-1062
##[6]
A. Ahmadian, N. Senu, F. Larki, S. Salahshour, A legendre approximation for solving a fuzzy fractional drug transduction model into the bloodstream, Recent Advances on Soft Computing and Data Mining, Springer International Publishing, 2014 (2014), 25-34
##[7]
A. Ahmadian, M. Suleiman, S. Salahshour, D. Baleanu, A Jacobi operational matrix for solving a fuzzy linear fractional differential equation, Adv. Difference Equ., 2013 (2013), 1-29
##[8]
T. Allahviranloo, A. Armand, Z. Gouyandeh, Fuzzy fractional differential equations under generalized fuzzy Caputo derivative, J. Intell. Fuzzy Systems, 26 (2014), 1481-1490
##[9]
A. K. Alomari, F. Awawdeh, N. Tahat, F. Bani Ahmad, W. Shatanawi, Multiple solutions for fractional differential equations: analytic approach, Appl. Math. Comput., 219 (2013), 8893-8903
##[10]
D. Alpay, V. Bolotnikov, H. T. Kaptanoğlu, The Schur algorithm and reproducing kernel Hilbert spaces in the ball, Linear Algebra Appl., 342 (2002), 163-186
##[11]
M. Al-Smadi, O. Abu Arqub, S. Momani, A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations, Math. Probl. Eng., 2013 (2013), 1-10
##[12]
S. Arshad, V. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Anal., 74 (2011), 3685-3693
##[13]
E. Babolian, H. Sadeghi, S. Javadi, Numerically solution of fuzzy differential equations by Adomian method, [[Numerical solution of fuzzy differential equations by the Adomian method]] Appl. Math. Comput., 149 (2004), 547-557
##[14]
S. Bartokos, Reproducing kernel Hilbert spaces, Diplomarbeit, University of Vienna, Fakultät für Mathematik BetreuerIn: Haslinger, Friedrich (2011)
##[15]
J. J. Buckley, E. Eslami, T. Feuring, Fuzzy mathematics in economics and engineering, Studies in Fuzziness and Soft Computing, Physica-Verlag, Heidelberg (2002)
##[16]
J. J. Buckley, Y. Qu, Solving systems of linear fuzzy equations , Fuzzy Sets and Systems, 43 (1991), 33-43
##[17]
Y. Chalco-Cano, H. Román-Flores, Some remarks on fuzzy differential equations via differential inclusions, Fuzzy Sets and Systems, 230 (2013), 3-20
##[18]
M.-G. Cui, Y.-Z. Lin, Nonlinear numerical analysis in the reproducing kernel space, Nova Science Publishers, Inc., New York (2009)
##[19]
V. Daftardar-Gejji, Y. Sukale, S. Bhalekar, Solving fractional delay differential equations: a new approach, Fract. Calc. Appl. Anal., 18 (2015), 400-418
##[20]
E. C. de Oliveira, J. A. Tenreiro Machado, A review of definitions for fractional derivatives and integral, Math. Probl. Eng., 2014 (2014), 1-6
##[21]
C. Gu, Penalized likelihood estimation: convergence under incorrect model, Statist. Probab. Lett., 36 (1998), 359-364
##[22]
J. R. Higgins, Sampling in reproducing kernel Hilbert space, New perspectives on approximation and sampling theory, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, (2014), 23-38
##[23]
H. Hult, Approximating some Volterra type stochastic integrals with applications to parameter estimation, Stochastic Process. Appl., 105 (2003), 1-32
##[24]
M. M. Khader, Numerical treatment for solving fractional logistic differential equation, Differ. Equ. Dyn. Syst., 24 (2016), 99-107
##[25]
A. Khastan, K. Ivaz, Numerical solution of fuzzy differential equations by Nyström method, Chaos Solitons Fractals, 41 (2009), 859-868
##[26]
E. Khodadadi, E. Çelik, The variational iteration method for fuzzy fractional differential equations with uncertainty, Fixed Point Theory Appl., 2013 (2013), 1-7
##[27]
M. P. Lazarević, R. R. Milan, B. S. Tomislav, Introduction to fractional calculus with brief historical background, Adv. Top. Appl. Fractional Calc. Control Probl. Syst. Stab. Model., 3 (2014), 82-85
##[28]
C.-L. Li, M.-G. Cui, The exact solution for solving a class nonlinear operator equations in the reproducing kernel space, Appl. Math. Comput., 143 (2003), 393-399
##[29]
M. Mazandarani, A.V. Kamyad, Modified fractional Euler method for solving fuzzy fractional initial value problem, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 12-21
##[30]
J. Mercer, Functions of positive and negative type, and their connection with the theory of integral equations, Trans. London Philosophical Soc. A, 209 (1909), 415-446
##[31]
O. H. Mohammed, F. S. Fadhel, F. A. Abdul-Khaleq, Differential transform method for solving fuzzy fractional initial value problems, J. Basrah Res., 37 (2011), 158-170
##[32]
S. Momani, Z. Odibat, Numerical approach to differential equations of fractional order, J. Comput. Appl. Math., 207 (2007), 96-110
##[33]
A. Salah, M. Khan, M. A. Gondal, A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method, Neural Comput. Appl., 23 (2013), 269-271
##[34]
S. Salahshour, T. Allahviranloo, Application of fuzzy differential transform method for solving fuzzy Volterra integral equations, Appl. Math. Model., 37 (2013), 1016-1027
##[35]
S. Salahshour, T. Allahviranloo, S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1372-1381
##[36]
D. J. Strauss, G. Steidl, Hybrid wavelet-support vector classification of waveforms, J. Comput. Appl. Math., 148 (2002), 375-400
##[37]
L.-H. Yang, M.-G. Cui, New algorithm for a class of nonlinear integro-differential equations in the reproducing kernel space, Appl. Math. Comput., 174 (2006), 942-960
##[38]
K. Yao, X.-W. Chen, A numerical method for solving uncertain differential equations, J. Intell. Fuzzy Systems, 25 (2013), 825-832
##[39]
Y. Zhang, G.-Y. Wang, Time domain methods for the solutions of n-order fuzzy differential equations, Fuzzy Sets and Systems, 94 (1998), 77-92
]
Variational approach to non-instantaneous impulsive nonlinear differential equations
Variational approach to non-instantaneous impulsive nonlinear differential equations
en
en
In this paper, a class of nonlinear differential equations with non-instantaneous impulses are considered. By using variational
methods and critical point theory, a criterion is obtained to guarantee that the non-instantaneous impulsive problem has
at least two distinct nonzero bounded weak solutions.
2440
2448
Liang
Bai
College of Mathematics
Taiyuan University of Technology
P. R. China
tj_bailiang@126.com
Juan J.
Nieto
Departamento de Estadística, Análisis Matemático y Optimización, Facultad de Matemáticas
Universidad de Santiago de Compostela
Spain
juanjose.nieto.roig@usc.es
Xiaoyun
Wang
College of Mathematics
Taiyuan University of Technology
P. R. China
wangxiaoyun@tyut.edu.cn
Non-instantaneous impulse
mountain pass theorem
bounded solution.
Article.14.pdf
[
[1]
G. A. Afrouzi, A. Hadjian, V. D. Rădulescu, Variational approach to fourth-order impulsive differential equations with two control parameters, Results Math., 65 (2014), 371-384
##[2]
G. A. Afrouzi, A. Hadjian, S. Shokooh, Infinitely many solutions for a Dirichlet boundary value problem with impulsive condition, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 77 (2015), 9-22
##[3]
L. Bai, J. J. Nieto, Variational approach to differential equations with not instantaneous impulses, Appl. Math. Lett., (2017), -
##[4]
G. Bonanno, R. Rodríguez-López, S. Tersian, Existence of solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 717-744
##[5]
V. Colao, L. Muglia, H.-K. Xu, Existence of solutions for a second-order differential equation with non-instantaneous impulses and delay, Ann. Mat. Pura Appl., 195 (2016), 697-716
##[6]
B.-X. Dai, D. Zhang, The existence and multiplicity of solutions for second-order impulsive differential equations on the half-line, Results Math., 63 (2013), 135-149
##[7]
E. Hernández, D. O’Regan, On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc., 141 (2013), 1641-1649
##[8]
J. Mawhin, M. Willem, Critical point theory and Hamiltonian systems, Applied Mathematical Sciences, Springer- Verlag, New York (1989)
##[9]
J. J. Nieto, Variational formulation of a damped Dirichlet impulsive problem, Appl. Math. Lett., 23 (2010), 940-942
##[10]
J. J. Nieto, D. O’Regan, variational approach to impulsive differential equations, Nonlinear Anal. Real World Appl., 10 (2009), 680-690
##[11]
M. Pierri, H. R. Henríquez, A. Prokopczyk, Global solutions for abstract differential equations with non-instantaneous impulses, Mediterr. J. Math., 13 (2016), 1685-1708
##[12]
M. Pierri, D. O’Regan, V. Rolnik, Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses, Appl. Math. Comput., 219 (2013), 6743-6749
##[13]
R. Rodríguez-López, S. Tersian, Multiple solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 1016-1038
##[14]
A. M. Samoilenko, N. A. Perestyuk, Impulsive differential equations, With a preface by Yu. A. Mitropolski˘ıand a supplement by S. I. Trofimchuk, Translated from the Russian by Y. Chapovsky, World Scientific Series on Nonlinear Science, Series A: Monographs and Treatises, World Scientific Publishing Co., Inc., River Edge, NJ (1995)
##[15]
J.-T. Sun, H.-B. Chen, Multiplicity of solutions for a class of impulsive differential equations with Dirichlet boundary conditions via variant fountain theorems, Nonlinear Anal. Real World Appl., 11 (2010), 4062-4071
##[16]
Y. Tian, W.-G. Ge, Applications of variational methods to boundary-value problem for impulsive differential equations, Proc. Edinb. Math. Soc., 51 (2008), 509-528
##[17]
E. Zeidler, Nonlinear functional analysis and its applications, III, Variational methods and optimization, Translated from the German by Leo F. Boron, Springer-Verlag, New York (1985)
]
A transformation algorithm for nonexpansive mappings
A transformation algorithm for nonexpansive mappings
en
en
A transformation algorithm is constructed for finding the fixed points of nonexpansive mappings. We show that the
suggested algorithm converges strongly to a fixed point of nonexpansive mappings under some different control conditions.
2449
2456
Xinhe
Zhu
Department of Mathematics
Tianjin Polytechnic University
China
zhumath@126.com
Shin Min
Kang
Center for General Education
Department of Mathematics and the RINS
China Medical University
Gyeongsang National University
Taiwan
Korea
smkang@gnu.ac.kr
Iterative method
nonexpansive mapping
fixed point.
Article.15.pdf
[
[1]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H.-K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014 ), 1-9
##[2]
K. Goebel, W. A. Kirk, Topics in Metric Fixed Point Theory: Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[3]
B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 73 (1967), 957-961
##[4]
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150
##[5]
P.-L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris Ser. A-B, 284 (1977), 1357-1359
##[6]
W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510
##[7]
A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
##[8]
T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl., 2005 (2005), 103-123
##[9]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[10]
H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[11]
H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-12
##[12]
Y.-H. Yao, R.-D. Chen, J.-C. Yao, Strong convergence and certain control conditions for modified Mann iteration, Nonlinear Anal., 68 (2008), 1687-1693
##[13]
Y.-H. Yao, Y.-C. Liou, T.-L. Lee, N.-C. Wong, An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex Anal., 17 (2016), 655-668
##[14]
Y.-H. Yao, N. Shahzad, New methods with perturbations for nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2011 (2011), 1-9
##[15]
Y.-H. Yao, N. Shahzad, Viscosity implicit midpoint methods for nonexpansive mappings, J. Nonlinear Sci. Appl., (In press), -
##[16]
Y.-H. Yao, N. Shahzad, Y.-C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015), 1-15
]
System of N fixed point operator equations with N-pseudo-contractive mapping in reflexive Banach spaces
System of N fixed point operator equations with N-pseudo-contractive mapping in reflexive Banach spaces
en
en
The purpose of this paper is to study the problem of the system of N fixed point operator equations with N-variables
pseudo-contractive mapping. Firstly, the concept of N-variables pseudo-contractive mapping and relatively concepts of nonlinear
mappings are presented in Banach spaces. Secondly, the existence theorems of solutions for the system of N fixed point operator
equations with N-variables pseudo-contractive mapping are proved in reflexive Banach spaces by using the method of product
spaces. In order to get the expected results, the normalized duality mapping of product Banach spaces is defined. Meanwhile the
reflexivity of the product of reflexive Banach spaces and Opial’s condition of product spaces of Banach spaces are also discussed.
2457
2470
Jinyu
Guan
Department of Mathematics, College of Science
Hebei North University
China
guanjinyu2010@163.com
Yanxia
Tang
Department of Mathematics, College of Science
Hebei North University
China
sutang2016@163.com
Yongchun
Xu
Department of Mathematics, College of Science
Hebei North University
China
hbxuyongchun@163.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
tjsuyongfu@163.com
N-variables pseudo-contractive mapping
N fixed point
system of operator equations
product spaces
reflexive Banach space
Opial’s condition.
Article.16.pdf
[
[1]
F. E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc., (1967), 875-882
##[2]
S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung, S. M. Kang, Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces, J. Math. Anal. Appl., 224 (1998), 149-165
##[3]
Y. J. Cho, S. M. Kang, X.-L. Qin, Some results on k-strictly pseudo-contractive mappings in Hilbert spaces, Nonlinear Anal., 70 (2009), 1956-1964
##[4]
K. Deimling, Zeros of accretive operators, Manuscripta Math., 13 (1974), 365-374
##[5]
J. García-Falset, E. Llorens-Fuster, Fixed points for pseudocontractive mappings on unbounded domains, Fixed Point Theory Appl., 2010 (2010), 1-17
##[6]
J. García-Falset, S. Reich, Zeroes of accretive operators and the asymptotic behavior of nonlinear semigroups, Houston J. Math., 32 (2006), 1179-1225
##[7]
J. S. Jung, Strong convergence of iterative methods for k-strictly pseudo-contractive mappings in Hilbert spaces, Appl. Math. Comput., 215 (2010), 3746-3753
##[8]
W. A. Kirk, R. Schöneberg, Zeros of m-accretive operators in Banach spaces, Israel J. Math., 35 (1980), 1-8
##[9]
H. Lee, S. Kim, Multivariate coupled fixed point theorems on ordered partial metric spaces, J. Korean Math. Soc., 51 (2014), 1189-1207
##[10]
L.-W. Li, W. Song, A hybrid of the extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces, Nonlinear Anal. Hybrid Syst., 1 (2007), 398-413
##[11]
C. Morales, Nonlinear equations involving m-accretive operators, J. Math. Anal. Appl., 97 (1983), 329-336
##[12]
C. H. Morales, The Leray-Schauder condition for continuous pseudo-contractive mappings, Proc. Amer. Math. Soc., 137 (2009), 1013-1020
##[13]
M. Osilike, A. Udomene, Demiclosedness principle and convergence theorems for strictly pseudocontractive mappings of Browder-Petryshyn type, J. Math. Anal. Appl., 256 (2001), 431-445
##[14]
N. Petrot, R. Wangkeeree, A general iterative scheme for strict pseudononspreading mapping related to optimization problem in Hilbert spaces, J. Nonlinear Anal. Optim., 2 (2011), 329-336
##[15]
Y.-F. Su, A note on ”Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings”, Nonlinear Anal., 70 (2009), 2519-2520
##[16]
Y.-F. Su, M.-Q. Li, New fixed point theorems for pseudocontractive mappings and zero point theorems for accretive operators in Banach spaces, Fixed Point Theory, 11 (2010), 129-132
##[17]
Y.-F. Su, A. Petruşel, J.-C. Yao, Multivariate fixed point theorems for contractions and nonexpansive mappings with applications, Fixed Point Theory Appl., 2016 (2016), 1-19
##[18]
W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
##[19]
W. Takahashi, Strong convergence theorems for maximal and inverse-strongly monotone mappings in Hilbert spaces and applications, J. Optim. Theory Appl., 157 (2013), 781-802
##[20]
Y.-C. Tang, J.-G. Peng, L.-W. Liu, Strong convergence theorem for pseudo-contractive mappings in Hilbert spaces, Nonlinear Anal., 74 (2011), 380-385
##[21]
S. Wang, A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces, Appl. Math. Lett., 24 (2011), 901-907
##[22]
Y.-H. Yao, Y.-C. Liou, Y.-P. Chen, Algorithms construction for nonexpansive mappings and inverse-strongly monotone mappings, Taiwanese J. Math., 15 (2011), 1979-1998
##[23]
Y.-H. Yao, Y.-C. Liou, G. Marino, A hybrid algorithm for pseudo-contractive mappings, Nonlinear Anal., 71 (2009), 4997-5002
##[24]
H. Zhang, Y.-F. Su, Convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces, Nonlinear Anal., 71 (2009), 4572-4580
##[25]
H. Zhang, Y.-F. Su, Strong convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces, Nonlinear Anal., 70 (2009), 3236-3242
##[26]
H.-Y. Zhou, Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces, Nonlinear Anal., 68 (2008), 2977-2983
##[27]
H.-Y. Zhou, Convergence theorems of fixed points for \(\kappa\)-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal., 69 (2008), 456-462
##[28]
H.-Y. Zhou, Y.-F. Su, Strong convergence theorems for a family of quasi-asymptotic pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 4047-4052
]
Lyapunov-type inequalities for fractional quasilinear problems via variational methods
Lyapunov-type inequalities for fractional quasilinear problems via variational methods
en
en
In this paper, by variational methods, some Lyapunov-type inequalities are established for fractional quasilinear problems
involving left and right Riemann-Liouville fractional derivative operators. To the authors’ knowledge, this is the first work,
where Lyapunov-type inequalities for fractional boundary value problems are investigated by using variational methods. As an
application of the obtained inequalities, we extend the notion of generalized eigenvalues to a fractional quasilinear system, and
we derive some geometric properties of the fractional generalized spectrum.
2471
2486
Mohamed
Jleli
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
Mokhtar
Kirane
LaSIE, Pole Sciences et Technologies
Université de La Rochelle
France
mkirane@univ-lr.fr
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Lyapunov inequality
fractional derivative
variational method
fractional quasilinear system
fractional generalized eigenvalues.
Article.17.pdf
[
[1]
M. F. Aktaş, Lyapunov-type inequalities for n-dimensional quasilinear systems, Electron. J. Differential Equations, 2013 (2013), 1-8
##[2]
N. Al Arifi, I. Altun, M. Jleli, A. Lashin, B. Samet, Lyapunov-type inequalities for a fractional p-Laplacian equation, J. Inequal. Appl., 2016 (2016), 1-11
##[3]
L. Bourdin, D. Idczak, A fractional fundamental lemma and a fractional integration by parts formula—Applications to critical points of Bolza functionals and to linear boundary value problems, Adv. Differential Equations, 20 (2015), 213-232
##[4]
R. C. Brown, D. B. Hinton, Lyapunov inequalities and their applications, Survey on classical inequalities, Math. Appl., Kluwer Acad. Publ., Dordrecht, 517 (2000), 1-25
##[5]
D. Çakmak, On Lyapunov-type inequality for a class of nonlinear systems, Math. Inequal. Appl., 16 (2013), 101-108
##[6]
D. Çakmak, A. Tiryaki, On lyapunov-type inequality for quasilinear systems, Appl. Math. Comput., 216 (2010), 3584-3591
##[7]
A. Chidouh, D. F. M. Torres, A generalized Lyapunov’s inequality for a fractional boundary value problem, J. Comput. Appl. Math., 312 (2017), 192-197
##[8]
P. L. De Nápoli, J. P. Pinasco, Estimates for eigenvalues of quasilinear elliptic systems, J. Differential Equations, 227 (2006), 102-115
##[9]
A . Elbert, On the half-linear second order differential equations, Acta. Math. Hungar., 49 (1987), 487-508
##[10]
R. A. C. Ferreira, A Lyapunov-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal., 16 (2013), 978-984
##[11]
R. A. C. Ferreira, On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function, J. Math. Anal. Appl., 412 (2014), 1058-1063
##[12]
D. Idczak, M. Majewski, Fractional fundamental lemma of order \(\alpha \in (n - 1/ 2 , n)\) with \(n\in \mathbb{N}, n\geq 2\), Dynam. Systems Appl., 21 (2012), 251-268
##[13]
M. Jleli, B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions, Math. Inequal. Appl., 18 (2015), 443-451
##[14]
A. Liapounoff, Probléme général de la stabilité du mouvement, (French) Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys., 9 (1907), 203-407
##[15]
D. O’Regan, B. Samet, Lyapunov-type inequalities for a class of fractional differential equations, J. Inequal. Appl., 2015 (2015), 1-10
##[16]
J. P. Pinasco, Lyapunov-type inequalities, With applications to eigenvalue problems, SpringerBriefs in Mathematics, Springer, New York (2013)
##[17]
M. H. Protter, The generalized spectrum of second-order elliptic systems, Rocky Mountain J. Math., 9 (1979), 503-518
##[18]
J. Rong, C.-Z. Bai, Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions, Adv. Difference Equ., 2015 (2015), 1-10
##[19]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Theory and applications, Edited and with a foreword by S. M. Nikolʹskiĭ, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon (1993)
##[20]
J. Sánchez, V. Vergara, A Lyapunov-type inequality for a \(\psi\) -Laplacian operator, Nonlinear Anal., 74 (2011), 7071-7077
##[21]
S. Sitho, S. K. Ntouyas, W. Yukunthorn, J. Tariboon, Lyapunov’s type inequalities for hybrid fractional differential equations, J. Inequal. Appl., 2016 (2016), 1-13
##[22]
X. H. Tang, X.-F. He, Lower bounds for generalized eigenvalues of the quasilinear systems, J. Math. Anal. Appl., 385 (2012), 72-85
##[23]
X.-J. Yang, J. A. Tenreiro Machado, A new fractional operator of variable order: application in the description of anomalous diffusion, Phys. A, 481 (2017), 276-283
]
On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales
On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales
en
en
We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some
basic properties of the HK delta integral for Riesz-space-valued functions are proved. Further, we prove uniform and monotone
convergence theorems.
2487
2500
Xuexiao
You
School of Mathematics and Statistics
College of Computer and Information
Hubei Normal University
Hohai University
P. R. China
P. R. China
youxuexiao@126.com
Dafang
Zhao
School of Mathematics and Statistics
College of Science
Hubei Normal University
Hohai University
P. R. China
P. R. China
dafangzhao@163.com
Delfim F. M.
Torres
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics
University of Aveiro
Portugal
delfim@ua.pt
Henstock-Kurzweil integral
Riesz space
time scales.
Article.18.pdf
[
[1]
G. Antunes Monteiro, A. Slavík, Generalized elementary functions, J. Math. Anal. Appl., 411 (2014), 838-852
##[2]
G. Antunes Monteiro, A. Slavík, Extremal solutions of measure differential equations, J. Math. Anal. Appl., 444 (2016), 568-597
##[3]
S. Avsec, B. Bannish, B. Johnson, S. Meckler, The Henstock-Kurzweil delta integral on unbounded time scales, PanAmer. Math. J., 16 (2006), 77-98
##[4]
R. G. Bartle, A modern theory of integration, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2001)
##[5]
N. Benkhettou, A. M. C. Brito da Cruz, D. F. M. Torres, A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration, Signal Process., 107 (2015), 230-237
##[6]
N. Benkhettou, A. M. C. Brito da Cruz, D. F. M. Torres, Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets, Math. Methods Appl. Sci., 39 (2016), 261-279
##[7]
A. Boccuto, Differential and integral calculus in Riesz spaces, Real functions, Liptovský Ján, (1996), Tatra Mt. Math. Publ., 14 (1998), 293-323
##[8]
A. Boccuto, Integration by parts with respect to the Henstock-Stieltjes in Riesz spaces, preprint, University of Perugia, (1999), 1-18
##[9]
A. Boccuto, D. Candeloro, B. Riečan, Abstract generalized Kurzweil-Henstock-type integrals for Riesz space-valued functions, Real Anal. Exchange, 34 (2009), 171-194
##[10]
A. Boccuto, D. Candeloro, A. R. Sambucini, A Fubini theorem in Riesz spaces for the Kurzweil-Henstock integral, J. Funct. Spaces Appl., 9 (2011), 283-304
##[11]
A. Boccuto, B. Riečan, A note on improper Kurzweil-Henstock integral in Riesz spaces, Acta Math. (Nitra), 5 (2002), 15-24
##[12]
A. Boccuto, B. Riečan, On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals, Czechoslovak Math. J., 54 (2004), 591-607
##[13]
A. Boccuto, B. Riečan, The Kurzweil-Henstock integral for Riesz space-valued maps defined in abstract topological spaces and convergence theorems, PanAmer. Math. J., 16 (2006), 63-79
##[14]
A. Boccuto, B. Riečan, M. Vrábelová, Kurzweil-Henstock integral in Riesz spaces, Bentham Science Publishers, United Arab Emirates (2009)
##[15]
A. Boccuto, V. A. Skvortsov, Henstock-Kurzweil type integration of Riesz-space-valued functions and applications toWalsh series, Real Anal. Exchange, 29 (2004), 419-438
##[16]
A. Boccuto, V. A. Skvortsov, Comparison of some Henstock-type integrals in the class of functions with values in Riesz spaces, (Russian); translated from Vestnik Moskov. Univ. Ser. I Mat. Mekh., 2006 (2006), 13–18, Moscow Univ. Math. Bull., 61 (2006), 12-17
##[17]
A. Boccuto, V. A. Skvortsov, On Kurzweil-Henstock type integrals with respect to abstract derivation bases for Rieszspace- valued functions, J. Appl. Funct. Anal., 1 (2006), 251-270
##[18]
A. Boccuto, V. A. Skvortsov, F. Tulone, Integration of functions with values in a complex Riesz space and some applications in harmonic analysis, (Russian); translated from Mat. Zametki, 98 (2015), 12–26, Math. Notes, 98 (2015), 25-37
##[19]
M. Bohner, T.-X. Li, Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient, Appl. Math. Lett., 37 (2014), 72-76
##[20]
M. Bohner, A. Peterson, Dynamic equations on time scales, An introduction with applications, Birkhäuser Boston, Inc., Boston, MA (2001)
##[21]
M. Bohner (Ed.), A. Peterson (Ed.), Advances in dynamic equations on time scales, Birkhäuser Boston, Inc., Boston, MA (2003)
##[22]
M. J. Bohner, S. H. Saker, Sneak-out principle on time scales, J. Math. Inequal., 10 (2016), 393-403
##[23]
B. Bongiorno, L. Di Piazza, K. Musiał, Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions, Math. Bohem., 131 (2006), 211-223
##[24]
P. S. Bullen, P. Y. Lee, J. L. Mawhin, P. Muldowney, W. F. Pfeffer, New integrals, Proceedings of the Henstock Conference held in Coleraine, Northern Ireland (1988)
##[25]
T. S. Chew, On Kurzweil generalized ordinary differential equations, J. Differential Equations, 76 (1988), 286-293
##[26]
M. Cichoń, On integrals of vector-valued functions on time scales, Commun. Math. Anal., 11 (2011), 94-110
##[27]
L. Di Piazza, K. Musiał, Relations among Henstock, McShane and Pettis integrals for multifunctions with compact convex values, Monatsh. Math., 173 (2014), 459-470
##[28]
M. Federson, J. G. Mesquita, A. Slavík, Measure functional differential equations and functional dynamic equations on time scales, J. Differential Equations, 252 (2012), 3816-3847
##[29]
D. H. Fremlin, A direct proof of the Matthes-Wright integral extension theorem, J. London Math. Soc., 11 (1975), 276-284
##[30]
R. A. Gordon, The integrals of Lebesgue,Denjoy, Perron, and Henstock , Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (1994)
##[31]
G. S. Guseinov, Integration on time scales, J. Math. Anal. Appl., 285 (2003), 107-127
##[32]
S. Heikkilä, Differential and integral equations with Henstock-Kurzweil integrable functions, J. Math. Anal. Appl., 379 (2011), 171-179
##[33]
S. Heikkilä, A. Slavík, On summability, multipliability, product integrability, and parallel translation, J. Math. Anal. Appl., 433 (2016), 887-934
##[34]
R. Henstock, A Riemann-type integral of Lebesgue power, Canad. J. Math., 20 (1968), 79-87
##[35]
R. Henstock, Lectures on the theory of integration, Series in Real Analysis,World Scientific Publishing Co., Singapore (1988)
##[36]
R. Henstock, The general theory of integration, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1991)
##[37]
S. Hilger, Ein Maß kettenkalkül mit Anwendung auf Zentrumannigfahigkeiten, Ph.D. Thesis, Universtät Würzburg (1988)
##[38]
D. S. Kurtz, C. W. Swartz, Theories of integration, The integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, Second edition, Series in Real Analysis, World Scientific Publishing Co. Pte. Ltd., , Hackensack, NJ (2012)
##[39]
J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, (Russian) Czechoslovak Math. J., 7 (1957), 418-449
##[40]
J. Kurzweil, Henstock-Kurzweil integration: its relation to topological vector spaces, Series in Real Analysis, World Scientific Publishing Co., Inc., River Edge, NJ (2000)
##[41]
J. Kurzweil, Generalized ordinary differential equations, Not absolutely continuous solutions, Series in Real Analysis, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2012)
##[42]
S. Leader, The Kurzweil-Henstock integral and its differentials, A unified theory of integration on \(\mathbb{R}\) and \(\mathbb{R}^n\). Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (2001)
##[43]
P. Y. Lee, Lanzhou lectures on Henstock integration, Series in Real Analysis, World Scientific Publishing Co., Inc., Teaneck, NJ (1989)
##[44]
T. Y. Lee, Henstock-Kurzweil integration on Euclidean spaces, Series in Real Analysis, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2011)
##[45]
P. Y. Lee, R. Výborný, Integral: an easy approach after Kurzweil and Henstock, Australian Mathematical Society Lecture Series, Cambridge University Press, Cambridge (2000)
##[46]
M. D. Ortigueira, D. F. M. Torres, J. J. Trujillo, Exponentials and Laplace transforms on nonuniform time scales, Commun. Nonlinear Sci. Numer. Simul., 39 (2016), 252-270
##[47]
A. Peterson, B. Thompson, Henstock-Kurzweil delta and nabla integrals, J. Math. Anal. Appl., 323 (2006), 162-178
##[48]
W. F. Pfeffer, The Riemann approach to integration, Local geometric theory, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge (1993)
##[49]
B. Riečan, On the Kurzweil integral for functions with values in ordered spaces, I, Acta Math. Univ. Comenian., 56/57 (1990), 75-83
##[50]
B. Riečan, T. Neubrunn, Integral, measure, and ordering, Appendix A by Ferdinand Chovanec and František Kôpka, Appendix B by Hana Kirchheimová and Zdenka Riečanová, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht; Ister Science, Bratislava (1997)
##[51]
B. Riečan, M. Vrábelová, On integration with respect to operator valued measures in Riesz spaces, Tatra Mt. Math. Publ., 2 (1993), 149-165
##[52]
B. Riečan, M. Vrábelová, On the Kurzweil integral for functions with values in ordered spaces, II, Math. Slovaca, 43 (1993), 471-475
##[53]
B. Riečan, M. Vrábelová, The Kurzweil construction of an integral in ordered spaces, Czechoslovak Math. J., 48 (1998), 565-574
##[54]
B. R. Satco, C. O. Turcu, Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on time scales, Math. Slovaca, 63 (2013), 1347-1360
##[55]
S. Schwabik, Generalized ordinary differential equations, Series in Real Analysis, World Scientific Publishing Co., Inc., River Edge, NJ (1992)
##[56]
S. Schwabik, G.-J. Ye, Topics in Banach space integration, Series in Real Analysis, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2005)
##[57]
A. Sikorska-Nowak, Integrodifferential equations on time scales with Henstock-Kurzweil-Pettis delta integrals, Abstr. Appl. Anal., 2010 (2010), 1-17
##[58]
A. Sikorska-Nowak, Integro-differential equations on time scales with Henstock-Kurzweil delta integrals, Discuss. Math. Differ. Incl. Control Optim., 31 (2011), 71-90
##[59]
A. Slavík, Generalized differential equations: differentiability of solutions with respect to initial conditions and parameters, J. Math. Anal. Appl., 402 (2013), 261-274
##[60]
A. Slavík, Kurzweil and McShane product integration in Banach algebras, J. Math. Anal. Appl., 424 (2015), 748-773
##[61]
A. Slavík, Well-posedness results for abstract generalized differential equations and measure functional differential equations, J. Differential Equations, 259 (2015), 666-707
##[62]
B. S. Thomson, Henstock-Kurzweil integrals on time scales, PanAmer. Math. J., 18 (2008), 1-19
##[63]
M. Vrábelová, B. Riečan, On the Kurzweil integral for functions with values in ordered spaces, III, Real functions, Liptovský Ján, (1994), Tatra Mt. Math. Publ., 8 (1996), 93-100
##[64]
G.-J. Ye, On Henstock-Kurzweil and McShane integrals of Banach space-valued functions, J. Math. Anal. Appl., 330 (2007), 753-765
##[65]
J. H. Yoon, On Henstock-Stieltjes integrals of interval-valued functions on time scales, J. Chungcheong Math. Soc., 29 (2016), 109-115
##[66]
D.-F. Zhao, G.-J. Ye, On AP-Henstock-Stieltjes integral, J. Chungcheong Math. Soc., 19 (2006), 177-187
]
Weak condition for generalized f-weakly Picard mappings on partial metric spaces
Weak condition for generalized f-weakly Picard mappings on partial metric spaces
en
en
Recently, Minak and Altun introduced the notions of multivalued weak contractions and multivalued weakly Picard operators
on partial metric spaces. They also obtained two fixed point theorems with the notions of multivalued (\(\delta\), L)– weak contractions
and multivalued (\(\alpha\), L)-weak contractions. In this paper, we introduce the notion of generalized multivalued (f, \(\alpha, \beta\))-weak
contraction on partial metric spaces. We also establish some coincidence and common fixed point theorems. Our results extend
and generalize some well-known common fixed point theorems on partial metric spaces.
2501
2509
Xinchen
Du
Department of Mathematics
Nanchang University
P. R. China
xcduncu@163.com
Xianjiu
Huang
Department of Mathematics
Nanchang University
P. R. China
xjhuangxwen@163.com
Chunfang
Chen
Department of Mathematics
Nanchang University
P. R. China
ccfygd@sina.com
Partial metric
common fixed point
hybrid maps
weakly Picard operators.
Article.19.pdf
[
[1]
Ö. Acar, I. Altun, Some generalizations of Caristi type fixed point theorem on partial metric spaces, Filomat, 26 (2012), 833-837
##[2]
Ö. Acar, I. Altun, S. Romaguera, Caristi’s type mappings on complete partial metric spaces, Fixed Point Theory, 14 (2013), 3-9
##[3]
Ö. Acar, V. Berinde, I. Altun, Fixed point theorems for Ćirić-type strong almost contractions on partial metric spaces, J. Fixed Point Theory Appl., 12 (2012), 247-259
##[4]
I. Altun, Ö. Acar, Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces, Topology Appl., 159 (2012), 2642-2648
##[5]
I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-10
##[6]
I. Altun, G. Minak, Mizoguchi-Takahashi type fixed point theorem on partial metric spaces, J. Adv. Math. Stud., 7 (2014), 80-88
##[7]
I. Altun, S. Romaguera, Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point, Appl. Anal. Discrete Math., 6 (2012), 247-256
##[8]
I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl., 157 (2010), 2778-2785
##[9]
H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology Appl., 159 (2012), 3234-3242
##[10]
H. Aydi, M. Abbas, C. Vetro, Common fixed points for multivalued generalized contractions on partial metric spaces, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 108 (2014), 483-501
##[11]
M. A. Bukatin, J. S. Scott, Towards computing distances between programs via Scott domains, Logical foundations of computer science, Yaroslavl, (1997), Lecture Notes in Comput. Sci., Springer, Berlin, 1234 (1997), 33-43
##[12]
M. A. Bukatin, S. Y. Shorina, Partial metrics and co-continuous valuations, Foundations of software science and computation structures, Lisbon, (1998), Lecture Notes in Comput. Sci., Springer, Berlin, 1378 (1998), 125-139
##[13]
L. Ćirić, B. Samet, H. Aydi, C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406
##[14]
W.-S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal., 73 (2010), 1439-1446
##[15]
R. H. Haghi, S. Rezapour, N. Shahzad, Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450-454
##[16]
X.-J. Huang, Y.-Y. Li, C.-X. Zhu, Multivalued f-weakly Picard mappings on partial metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 1234-1244
##[17]
E. Karapınar, ˙I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894-1899
##[18]
S. G. Matthews, Partial metric topology, Papers on general topology and applications, Flushing, NY, (1992), Ann. New York Acad. Sci., New York Acad. Sci., New York, 728 (1994), 183-197
##[19]
G. Minak, I. Altun, Multivalued weakly Picard operators on partial metric spaces, Nonlinear Funct. Anal. Appl., 19 (2014), 45-59
##[20]
S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
##[21]
S. Oltra, O. Valero, Banach’s fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste, 36 (2004), 17-26
##[22]
S. Romaguera, Matkowski’s type theorems for generalized contractions on (ordered) partial metric spaces, Appl. Gen. Topol., 12 (2011), 213-220
##[23]
S. Romaguera, Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl., 159 (2012), 194-199
##[24]
S. Romaguera, On Nadler’s fixed point theorem for partial metric mpaces, Math. Sci. Appl. E-Notes, 1 (2013), 1-8
##[25]
S. Romaguera, M. Schellekens, Duality and quasi-normability for complexity spaces, Appl. Gen. Topol., 3 (2002), 91-112
##[26]
S. Romaguera, M. Schellekens, Weightable quasi-metric semigroups and semilattices, Electron. Notes Theor. Comput. Sci., 40 (2003), 347-358
##[27]
B. Samet, M. Rajović, R. Lazović, R. Stojiljković, Common fixed-point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-14
##[28]
M. P. Schellekens, A characterization of partial metrizability: domains are quantifiable, Topology in computer science, Schloß Dagstuhl, (2000). Theoret. Comput. Sci., 305 (2003), 409-432
##[29]
M. P. Schellekens, The correspondence between partial metrics and semivaluations, Theoret. Comput. Sci., 315 (2004), 135-149
##[30]
W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling, 55 (2012), 680-687
##[31]
O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol., 6 (2005), 229-240
##[32]
X. Wen, X.-J. Huang, Common fixed point theorem under contractions in partial metric spaces, J. Comput. Anal. Appl., 13 (2011), 583-589
]
Fixed point property for digital spaces
Fixed point property for digital spaces
en
en
The paper compares the fixed point property (FPP for short) of a compact Euclidean plane with its digital versions associated
with Khalimsky and Marcus-Wyse topology. More precisely, by using a Khalimsky and a Marcus-Wyse topological digitization,
the paper studies digital versions of the FPP for Euclidean topological spaces. Besides, motivated by the digital homotopy fixed
point property (DHFP for brevity) [O. Ege, I. Karaca, C. R. Math. Acad. Sci. Paris, 353 (2015), 1029–1033], the present paper
establishes the digital homotopy almost fixed point property (DHAFP for short) which is more generalized than the DHFP.
Moreover, the present paper corrects some errors in [O. Ege, I. Karaca, C. R. Math. Acad. Sci. Paris, 353 (2015), 1029–1033] and
improves it.
2510
2523
Sang-Eon
Han
Department of Mathematics Education, Institute of Pure and Applied Mathematics
Chonbuk National University
Republic of Korea
sehan@jbnu.ac.kr
Digital space
digitization
Khalimsky topology
Marcus-Wyse topology
fixed point property
digital homotopy almost fixed point property
almost fixed point property.
Article.20.pdf
[
[1]
P. Alexandroff, Diskrete räume, Mat. Sb. (N.S.), 2 (1937), 501-518
##[2]
L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vision, 10 (1999), 51-62
##[3]
O. Ege, I. Karaca, Digital homotopy fixed point theory, C. R. Math. Acad. Sci. Paris, 353 (2015), 1029-1033
##[4]
S.-E. Han, On the classification of the digital images up to a digital homotopy equivalence, J. Comput. Commun. Res., 10 (2000), 194-207
##[5]
S.-E. Han, Non-product property of the digital fundamental group, Inform. Sci., 171 (2005), 73-91
##[6]
S.-E. Han, Fixed point theorems for digital images, Honam Math. J., 37 (2015), 595-608
##[7]
S.-E. Han, Contractibility and fixed point property: the case of Khalimsky topological spaces, Fixed Point Theory Appl., 2016 (2016), 1-20
##[8]
S.-E. Han, Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces, J. Nonlinear Sci. Appl., 10 (2017), 34-47
##[9]
S.-E. Han, B. G. Park, Digital graph \((k_0, k_1)\)-isomorphism and its applications, Summer conference on topology and its application, USA (2003)
##[10]
G. T. Herman, Oriented surfaces in digital spaces, CVGIP: Graph. Model. Im. Proc., 55 (1993), 381-396
##[11]
J. M. Kang, S.-E. Han, K. C. Min, Digitizations associated with several types of digital topological approaches, Comput. Appl. Math., 36 (2017), 571-597
##[12]
E. D. Khalimsky, Applications of connected ordered topological spaces in topology, Conference of Mathematics Departments of Povolsia, (1970)
##[13]
E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl., 36 (1990), 1-17
##[14]
T. Y. Kong, A. Rosenfeld, Topological algorithms for digital image processing, Elsevier Science, Amsterdam (1996)
##[15]
V. Kovalevsky, Axiomatic digital topology, J. Math. Imaging Vision, 26 (2006), 41-58
##[16]
J. R. Munkres, Topology, Second edition, Prentice Hall , NJ (2000)
##[17]
A. Rosenfeld, Digital topology, Amer. Math. Monthly, 86 (1979), 76-87
##[18]
A. Rosenfeld, Continuous functions on digital pictures, Pattern Recognit. Lett., 4 (1986), 177-184
##[19]
S. Samieinia, The number of Khalimsky-continuous functions between two points, Combinatorial image analysis, Lecture Notes in Comput. Sci., Springer, Heidelberg, 6636 (2011), 96-106
##[20]
J. Šlapal, Topological structuring of the digital plane, Discrete Math. Theor. Comput. Sci., 5 (2013), 165-176
##[21]
M. Szymik, Homotopies and the universal fixed point property, Order, 32 (2015), 301-311
##[22]
F. Wyse, D. Marcus, Solution to problem 5712, Amer. Math. Monthly, 77 (1970), 11-19
]
Some explicit identities for the modified higher-order degenerate q-Euler polynomials and their zeroes
Some explicit identities for the modified higher-order degenerate q-Euler polynomials and their zeroes
en
en
Recently, Kim et al. [D. S. Kim, T. Kim, Ars Combin., 126 (2016), 435–441], [D. S. Kim, T. Kim, J. Nonlinear Sci. Appl.,
9 (2016), 443–451], [T. Kim, D. S. Kim, H.-I. Kwon, Filomat, 30 (2016), 905–912] and [T. Kim, D. S. Kim, H.-I. Kwon, J.-J. Seo,
D. V. Dolgy, J. Nonlinear Sci. Appl., 9 (2016), 1077–1082] studied symmetric identities of higher-order degenerate q-Euler
polynomials. In this paper, we define the modified higher-order degenerate q-Euler polynomials and give some identities for
these polynomials. Also we give numerical investigations of the zeroes of the modified higher-order q-Euler polynomials and
the zeroes of the modified higher-order degenerate q-Euler polynomials.
Furthermore, we demonstrate the shapes and zeroes of the modified higher-order q-Euler polynomials and the modified
higher-order degenerate q-Euler polynomials by using a computer.
2524
2538
L. C.
Jang
Graduate School of Education
Konkuk University
Republic of Korea
lcjang@konkuk.ac.kr
B. M.
Kim
Department of Mechanical System Engineering
Dongguk University
Korea
kbm713@dongguk.ac.kr
S. K.
Choi
Department of Mathematics Education
Konkuk University
Republic of Korea
schoi@konkuk.ac.kr
C. S.
Ryoo
Department of Mathematics
Hannam University
Republic of Korea
ryoocs@hnu.kr
D. V.
Dolgy
Hanrimwon
Institute of Natural Sciences
Kwangwoon University
Far eastern Federal University
Republic of Korea
Russia
d_dol@mail.ru
Identities of symmetry
modified q-Euler polynomials
modified higher-order degenerate q-Euler polynomials.
Article.21.pdf
[
[1]
W. A. Al-Salam, q-Bernoulli numbers and polynomials, Math. Nachr., 17 (1959), 239-260
##[2]
A. Bayad, J. Chikhi, Apostol-Euler polynomials and asymptotics for negative binomial reciprocals, Adv. Stud. Contemp. Math. (Kyungshang), 24 (2014), 33-37
##[3]
L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J., 15 (1948), 987-1000
##[4]
L. Carlitz, q-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc., 76 (1954), 332-350
##[5]
L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51-88
##[6]
W. S. Chung, M. Jung, Some properties concerning q-derivatives and q-Hermite polynomial, Adv. Stud. Contemp. Math. (Kyungshang), 24 (2014), 149-153
##[7]
D. Ding, J.-Z. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 20 (2010), 7-21
##[8]
L.-C. Jang, A family of Barnes-type multiple twisted q-Euler numbers and polynomials related to Fermionic p-adic invariant integrals on \(\mathbb{Z}_p\), J. Comput. Anal. Appl., 13 (2011), 376-387
##[9]
J. H. Jin, T. Mansour, E.-J. Moon, J.-W. Park, On the (r, q)-Bernoulli and (r, q)-Euler numbers and polynomials, J. Comput. Anal. Appl., 19 (2015), 250-259
##[10]
T. Kim, Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 93-96
##[11]
T. Kim, Barnes-type multiple q-zeta functions and q-Euler polynomials, J. Phys. A, 43 (2010), 1-11
##[12]
T. Kim, New approach to q-Euler polynomials of higher order, Russ. J. Math. Phys., 17 (2010), 218-225
##[13]
T. Kim, A study on the q-Euler numbers and the fermionic q-integral of the product of several type q-Bernstein polynomials on \(\mathbb{Z}_p\), Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 5-11
##[14]
T. Kim, On degenerate q-Bernoulli polynomials, Bull. Korean Math. Soc., 53 (2016), 1149-1156
##[15]
D. S. Kim, T. Kim, Barnes-type Boole polynomials, Contrib. Discrete Math., 11 (2016), 7-15
##[16]
D. S. Kim, T. Kim, Generalized Boole numbers and polynomials, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 110 (2016), 823-839
##[17]
D. S. Kim, T. Kim, Some identities of symmetry for q-Bernoulli polynomials under symmetric group of degree n, Ars Combin., 126 (2016), 435-441
##[18]
D. S. Kim, T. Kim, Symmetric identities of higher-order degenerate q-Euler polynomials, J. Nonlinear Sci. Appl., 9 (2016), 443-451
##[19]
T. Kim, D. S. Kim, H.-I. Kwon, Some identities relating to degenerate Bernoulli polynomials, Filomat, 30 (2016), 905-912
##[20]
T. Kim, D. S. Kim, H.-I. Kwon, J.-J. Seo, D. V. Dolgy, Some identities of q-Euler polynomials under the symmetric group of degree n, J. Nonlinear Sci. Appl., 9 (2016), 1077-1082
##[21]
J. G. Lee, L.-C. Jang, On modified degenerate Carlitz q-Bernoulli numbers and polynomials, Adv. Difference Equ., 2017 (2017), 1-9
##[22]
Q.-M. Luo, q-analogues of some results for the Apostol-Euler polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 20 (2010), 103-113
##[23]
A. Sharma, q-Bernoulli and Euler numbers of higher order, Duke Math. J., 25 (1958), 343-353
##[24]
K. Sharma, q-fractional integrals and special functions, Adv. Stud. Contemp. Math. (Kyungshang), 24 (2014), 87-95
##[25]
N.-L. Wang, C. Li, H.-L. Li, Some identities on the generalized higher-order Euler and Bernoulli numbers, Ars Combin., 102 (2011), 517-528
##[26]
M. Wu, S. S. Du, A symmetric identity for degenerate higher-order Bernoulli polynomials and generalized power sum polynomials, (Chinese) Math. Pract. Theory, 44 (2014), 256-261
]
Positive solutions of a weakly singular periodic eco-economic system with changing-sign perturbation
Positive solutions of a weakly singular periodic eco-economic system with changing-sign perturbation
en
en
In this paper, we establish the positive bounded solutions for a changing-sign periodic perturbed differential system with
weak singularity in eco-economic and other applied fields. The conditions for the existence of solution are established for the
positive, negative and semipositone cases of nonlinear term, and the perturbation is allowed to be a singular and changing-sign
\(L^1(0, T)\) function.
2539
2549
Teng
Ren
School of Logistics and Transportation
Central South University of Forestry and Technology
China
chinarenteng@163.com;hunantengren@163.com
Sidi
Li
School of Tourism Management
Central South University of Forestry and Technology
China
sidilihunan@163.com
Xinguang
Zhang
School of Mathematical and Informational Sciences
Department of Mathematics and Statistics
Yantai University
Curtin University of Technology
China
Australia
zxg123242@163.com
Weak singularity
bounded solutions
sign-changing perturbation
periodic problems
eco-economical system.
Article.22.pdf
[
[1]
Z.-B. Bai, Solvability for a class of fractional m-point boundary value problem at resonance, Comput. Math. Appl., 62 (2011), 1292-1302
##[2]
Z.-B. Bai, Eigenvalue intervals for a class of fractional boundary value problem, Comput. Math. Appl., 64 (2012), 3253-3257
##[3]
Z.-B. Bai, Y.-H. Zhang, The existence of solutions for a fractional multi-point boundary value problem, Comput. Math. Appl., 60 (2010), 2364-2372
##[4]
Z.-W. Cao, D.-Q. Jiang, Periodic solutions of second order singular coupled systems, Nonlinear Anal., 71 (2009), 3661-3667
##[5]
Y.-J. Cui, Computation of topological degree in ordered Banach spaces with lattice structure and applications, Appl. Math., 58 (2013), 689-702
##[6]
Y.-J. Cui, Uniqueness of solution for boundary value problems for fractional differential equations, Appl. Math. Lett., 51 (2016), 48-54
##[7]
Y.-J. Cui, L.-S. Liu, X.-Q. Zhang, Uniqueness and existence of positive solutions for singular differential systems with coupled integral boundary value problems, Abstr. Appl. Anal., 2013 (2013), 1-9
##[8]
Y.-J. Cui, J.-X. Sun, Fixed point theorems for a class of nonlinear operators in Hilbert spaces and applications, Positivity, 15 (2011), 455-464
##[9]
Y.-J. Cui, J.-X. Sun, Fixed point theorems for a class of nonlinear operators in Hilbert spaces with lattice structure and application, Fixed Point Theory Appl., 2013 (2013), 1-9
##[10]
Y.-J. Cui, J.-X. Sun, Y.-M. Zou, Global bifurcation and multiple results for Sturm-Liouville problems, J. Comput. Appl. Math., 235 (2011), 2185-2192
##[11]
Y.-J. Cui, Y.-M. Zou, Existence of solutions for second-order integral boundary value problems, Nonlinear Analysis: Modelling and Control, 21 (2016), 828-838
##[12]
Y.-J. Cui, Y.-M. Zou, An existence and uniqueness theorem for a second order nonlinear system with coupled integral boundary value conditions, Appl. Math. Comput., 256 (2015), 438-444
##[13]
Y.-J. Cui, Solvability of second-order boundary-value problems at resonance involving integral conditions, Electronic Journal of Differential Equations, 2012 (2012), 1-9
##[14]
A. Demir, A. Mehrotra, J. Roychowdhury, Phase noise in oscillators: A unifying theory and numerical methods for characterization, IEEE Trans. Circuits Syst. Fundam. Theory Appl., 47 (2000), 655-674
##[15]
C. W. Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, Third edition, Springer Series in Synergetics, Springer-Verlag, Berlin (2004)
##[16]
X.-A. Hao, L.-S. Liu, Y.-H. Wu, Existence and multiplicity results for nonlinear periodic boundary value problems, Nonlinear Anal., 72 (2010), 3635-3642
##[17]
V. G. Ivancevic, T. T. Ivancevic, Geometrical dynamics of complex systems: a unified modelling approach to physics, control, biomechanics, neurodynamics and psycho-socio-economical dynamics, Springer Science & Business Media, (2006)
##[18]
H.-Y. Li, J.-X. Sun, Positive solutions of superlinear semipositone nonlinear boundary value problems, Comput. Math. Appl., 61 (2011), 2806-2815
##[19]
H.-Y. Li, F. Sun, Existence of solutions for integral boundary value problems of second-order ordinary differential equations, Bound. Value Probl., 2012 (2012), 1-7
##[20]
Y. Loya, Recolonization of Red Sea corals affected by natural catastrophes and manmade perturbations, Ecol., 57 (1976), 278-289
##[21]
W. Moon, J. S. Wettlaufer, A stochastic perturbation theory for non-autonomous systems, J. Math. Phys., 54 (2013), 1-31
##[22]
D.-B. Qian, L. Chen, X.-Y. Sun, Periodic solutions of superlinear impulsive differential equations: a geometric approach, J. Differential Equations, 258 (2015), 3088-3106
##[23]
S.-T. Qin, X.-P. Xue, Periodic solutions for nonlinear differential inclusions with multivalued perturbations, J. Math. Anal. Appl., 424 (2015), 988-1005
##[24]
J.-X. Sun, Y.-J. Cui, Fixed point theorems for a class of nonlinear operators in Riesz spaces, Fixed Point Theory, 14 (2013), 185-192
##[25]
P. J. Torres, Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem, J. Differential Equations, 190 (2003), 643-662
##[26]
J. R.Ward, Jr., Periodic solutions of ordinary differential equations with bounded nonlinearities, Topol. Methods Nonlinear Anal., 19 (2002), 275-282
##[27]
X.-G. Zhang, L.-S. Liu, Y.-H. Wu, Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives, Appl. Math. Comput., 219 (2012), 1420-1433
##[28]
X.-G. Zhang, L.-S. Liu, Y.-H. Wu, Multiple positive solutions of a singular fractional differential equation with negatively perturbed term, Math. Comput. Modelling, 55 (2012), 1263-1274
##[29]
X.-G. Zhang, Y.-H. Wu, L. Caccetta, Nonlocal fractional order differential equations with changing-sign singular perturbation, Appl. Math. Modelling, 39 (2015), 6543-6552
]
Common fixed points for multivalued mappings in G-metric spaces with applications
Common fixed points for multivalued mappings in G-metric spaces with applications
en
en
In this paper, we define new notions called (g-F) contractions and generalize Mizoguchi-Takahashi contractions for complete
G-metric spaces and we establish some new coincidence points and common fixed point results. Our results unify and generalize
various known comparable results from the current literature. An example and application are given to illustrate the usability
of the main results.
2550
2564
Z.
Mustafa
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
zead@qu.edu.qa
M.
Arshad
Department of Mathematics
International Islamic University
Pakistan
marshadzia@iiu.edu.pk
S. U.
Khan
Department of Mathematics
Department of Mathematics
International Islamic University
Gomal University D. I. Khan
Pakistan
Pakistan
gomal85@gmail.com
J.
Ahmad
Department of Mathematics
University of Jeddah
Saudi Arabia
jamshaid_jasim@yahoo.com
M.
Jaradat
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
mmjst4@qu.edu.qa
G-metric space
fixed point
F-contraction
(g-F) contraction.
Article.23.pdf
[
[1]
M. Abbas, B. Ali, S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-11
##[2]
M. Abbas, T. Nazir, W. Shatanawi, Z. Mustafa, Fixed and related fixed point theorems for three maps in G-metric spaces, Hacet. J. Math. Stat., 41 (2012), 291-306
##[3]
M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22 (2009), 511-515
##[4]
Ö. Acar, I. Altun, A fixed point theorem for multivalued mappings with \(\delta\)-distance, Abstr. Appl. Anal., 2014 (2014), 1-5
##[5]
M. Arshad, S. U. Khan, J. Ahmad, Fixed point results for f-contractions involving some new rational expressions, JP J. Fixed Point Theory Appl., 11 (2016), 79-97
##[6]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[7]
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37
##[8]
L. B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273
##[9]
B. C. Dhage, Generalised metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc., 84 (1992), 329-336
##[10]
M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74-79
##[11]
B. Fisher, Set-valued mappings on metric spaces, Fund. Math., 112 (1981), 141-145
##[12]
M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), 604-608
##[13]
L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
##[14]
N. Hussain, J. Ahmad, L. Ćirić, A. Azam, Coincidence point theorems for generalized contractions with application to integral equations, Fixed Point Theory Appl., 2015 (2015), 1-13
##[15]
A. Hussain, M. Arshad, S. U. Khan, \(\tau\)-Generalization of fixed point results for F-contraction, Bangmod Int. J. Math. Comp. Sci., 1 (2015), 127-137
##[16]
N. Hussain, E. Karapınar, P. Salimi, F. Akbar, \(\alpha\)-admissible mappings and related fixed point theorems, J. Inequal. Appl., 2013 (2013), 1-11
##[17]
N. Hussain, P. Salimi, Suzuki-Wardowski type fixed point theorems for \(\alpha\)-GF-contractions, Taiwanese J. Math., 18 (2014), 1879-1895
##[18]
M. Javahernia, A. Razani, F. Khojasteh, Common fixed point of the generalized Mizoguchi-Takahashi’s type contractions, Fixed Point Theory Appl., 2014 (2014), 1-12
##[19]
A. Kaewcharoen, A. Kaewkhao, Common fixed points for single-valued and multi-valued mappings in G-metric spaces, Int. J. Math. Anal. (Ruse), 5 (2011), 1775-1790
##[20]
S. U. Khan, M. Arshad, A. Hussain, M. Nazam, Two new types of fixed point theorems for F-contraction, J. Adv. Stud. Topol., 7 (2016), 251-260
##[21]
W. A. Kirk, Some recent results in metric fixed point theory, J. Fixed Point Theory Appl., 2 (2007), 195-207
##[22]
Z. Mustafa, T. V. An, N. V. Dung, L. T. Quan, Two fixed point theorems for maps on incomplete G-metric spaces, Appl. Math. Sci. (Ruse), 7 (2013), 2271-2281
##[23]
Z. Mustafa, H. Aydi, E. Karapınar, Generalized Meir-Keeler type contractions on G-metric spaces, Appl. Math. Comput., 219 (2013), 10441-10447
##[24]
Z. Mustafa, V. Parvaneh, M. Abbas, J. R. Roshan, Some coincidence point results for generalized (\(\psi,\phi\))-weakly contractive mappings in ordered G-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-23
##[25]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297
##[26]
S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
##[27]
M. Nazam, M. Arshad, On a fixed point theorem with application to integral equations, Int. J. Anal., 2016 (2016), 1-7
##[28]
M. Nazam, M. Arshad, M. Abbas, Some fixed point results for dualistic rational contractions, Appl. Gen. Topol., 17 (2016), 199-209
##[29]
H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
##[30]
S. Radenović, B. E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Comput. Math. Appl., 57 (2009), 1701-1707
##[31]
K. P. R. Rao, K. B. Lakshmi, Z. Mustafa, A unique common fixed point theorem for six maps in G-metric spaces, Internat. J. Nonlinear Anal. Appl., 3 (2012), 17-23
##[32]
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] by L.-G. Huang and X. Zhang, J. Math. Anal. Appl., 345 (2008), 719-724
##[33]
N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl., 2013 (2013), 1-13
##[34]
N. Tahat, H. Aydi, E. Karapınar, W. Shatanawi, Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-9
##[35]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-6
]
Robust state estimation for neutral-type neural networks with mixed time delays
Robust state estimation for neutral-type neural networks with mixed time delays
en
en
In this paper, the state estimation problem is dealt with a class of neutral-type Markovian neural networks with mixed time
delays. The network systems have a finite number of modes, and the modes may jump from one state to another according to a
Markov chain. We are devoted to design a state estimator to estimate the neuron states, through available output measurements,
such that the dynamics of the estimation error is globally asymptotically stable in the mean square. From the Lyapunov-
Krasovskii functional and linear matrix inequality (LMI) approach, we establish sufficient conditions to guarantee the existence
of the state estimators. Furthermore, it is shown that the traditional stability analysis issue for delayed neural networks with
Markovian chains can be included as a special case of our main results. A simulation shows the usefulness of the derived
LMI-based stability conditions.
2565
2578
Bo
Du
Department of Mathematics
Huaiyin Normal University
P. R. China
dubo7307@163.com
Wenbing
Zhang
Department of Mathematics
Yangzhou University
P. R. China
zwb850506@126.com
Qing
Yang
Department of Mathematics
Huaiyin Normal University
P. R. China
yangqing3511115@163.com
Neutral-type
Markovian jumping system
Lyapunov functional method
stability.
Article.24.pdf
[
[1]
S. Arik, Global robust stability analysis of neural networks with discrete time delays, Chaos Solitons Fractals, 26 (2005), 1407-1414
##[2]
S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1994)
##[3]
A.-P. Chen, J.-D. Cao, L.-H. Huang, Global robust stability of interval cellular neural networks with time-varying delays, Chaos Solitons Fractals, 23 (2005), 787-799
##[4]
A.-P. Chen, L.-H. Huang, J.-D. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., 137 (2003), 177-193
##[5]
C.-J. Cheng, T.-L. Liao, J.-J. Yan, C.-C. Hwang, Globally asymptotic stability of a class of neutral-type neural networks with delays, IEEE Trans. Systems Man Cybernet., 36 (2006), 1191-1195
##[6]
V. T. S. Elanayar, Y. C. Shin, Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems, IEEE Trans. Neural Netw., 5 (1994), 594-603
##[7]
K. Gu, An integral inequality in the stability problem of time-delay systems, Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, 3 (2000), 2805-2810
##[8]
R. Habtom, L. Litz, Estimation of unmeasured inputs using recurrent neural networks and the extended Kalman filter, International Conference on Neural Networks, Houston, TX, 4 (1997), 2067-2071
##[9]
J. Hale, Theory of functional differential equations, Second edition, Applied Mathematical Sciences, Springer-Verlag, New York-Heidelberg (1977)
##[10]
Y.-D. Ji, H. J. Chizeck, Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control, IEEE Trans. Automat. Control, 35 (1990), 777-788
##[11]
M. P. Kennedy, L. O. Chua, Neural networks for nonlinear programming, IEEE Trans. Circuits and Systems, 35 (1988), 554-562
##[12]
N. N. Krasovskiĭ, E. A. Lidskiĭ, Analytical design of controllers in systems with random attributes, I, Statement of the problem, method of solving, Avtomat. i Telemeh., 22, 1145–1150, (Russian. English summary); translated as Automat. Remote Control, 22 (1961), 1021-2025
##[13]
Y.-R. Liu, Z.-D. Wang, X.-H. Liu, Design of exponential state estimators for neural networks with mixed time delays, Phys. Lett. A, 364 (2007), 401-412
##[14]
Y.-R. Liu, Z.-D. Wang, X.-H. Liu, Exponential synchronization of complex networks with Markovian jump and mixed delays, Phys. Lett. A, 372 (2008), 3986-3998
##[15]
Y.-R. Liu, Z.-D. Wang, X.-H. Liu, Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays, Neurocomputing, 94 (2012), 46-53
##[16]
G.-Q. Liu, S. X. Yang, W. Fu, New robust stability of uncertain neutral-type neural networks with discrete interval and distributed time-varying delays, J. Comput., 7 (2012), 264-271
##[17]
X.-Y. Lou, B.-T. Cui, Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters, Chaos Solitons Fractals, 39 (2009), 2188-2197
##[18]
C. M. Marcus, R. M. Westervelt, Stability of analog neural networks with delay, Phys. Rev. A, 39 (1989), 347-359
##[19]
S.-S. Mou, H.-J. Gao, W.-Y. Qiang, Z.-Y. Fei, State estimation for discrete-time neural networks with time-varying delays, Neurocomputing, 72 (2008), 643-647
##[20]
Y. Niu, J. Lam, X. Wang, Sliding-mode control for uncertain neutral delay systems, IEE Proc. Control Theory Appl., 151 (2004), 38-44
##[21]
J. H. Park, Further result on asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays, Appl. Math. Comput., 182 (2006), 1661-1666
##[22]
J. H. Park, C. H. Park, O. M. Kwon, S. M. Lee, A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput., 199 (2008), 716-722
##[23]
R. Rakkiyappan, P. Balasubramaniam, J.-D. Cao, Global exponential stability results for neutral-type impulsive neural networks, Nonlinear Anal. Real World Appl., 11 (2010), 122-130
##[24]
F. M. Salam, J.-H. Zhang, Adaptive neural observer with forward co-state propagation, Proceedings of the International Joint Conference on Neural Networks, Washington, DC, 1 (2001), 675-680
##[25]
V. Singh, Global robust stability of delayed neural networks: estimating upper limit of norm of delayed connection weight matrix, Chaos Solitons Fractals, 32 (2007), 259-263
##[26]
A. V. Skorokhod, Asymptotic methods in the theory of stochastic differential equations, Translated from the Russian by H. H. McFaden, Translations of Mathematical Monographs, American Mathematical Society, , Providence, RI (1989)
##[27]
Y.-L. Wang, J.-D. Cao, Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems, Nonlinear Anal. Real World Appl., 14 (2013), 842-851
##[28]
Z.-D.Wang, D.W. C. Ho, X.-H. Liu, State estimation for delayed neural networks, IEEE Trans. Neural Netw., 16 (2005), 279-286
##[29]
Z.-D. Wang, Y.-R. Liu, X.-H. Liu, State estimation for jumping recurrent neural networks with discrete and distributed delays, Neural Netw., 22 (2009), 41-48
##[30]
B. Wang, X.-Z. Liu, S.-M. Zhong, New stability analysis for uncertain neutral system with time-varying delay, Appl. Math. Comput., 197 (2008), 457-465
##[31]
Z.-H. Xia, X.-H.Wang, X.-M. Sun, B.-W.Wang, Steganalysis of least significant bit matching using multiorder differences, Secur. Commun. Netw., 7 (2014), 1283-1291
##[32]
Z.-H. Xia, X.-H. Wang, X.-M. Sun, Q. Wang, A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data, IEEE Trans. Parallel Distrib. Syst., 27 (2015), 340-352
##[33]
K.-W. Yu, C.-H. Lien, Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos Solitons Fractals, 38 (2008), 650-657
##[34]
Q. Zhang, X.-P. Wei, J. Xu, Delay-dependent global stability results for delayed Hopfield neural networks, Chaos Solitons Fractals, 34 (2007), 662-668
##[35]
Q. Zhang, X.-P. Wei, J. Xu, Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays, Chaos Solitons Fractals, 36 (2008), 985-990
##[36]
Q. Zhang, X.-P.Wei, J. Xu, Exponential stability for nonautonomous neural networks with variable delays, Chaos Solitons Fractals, 39 (2009), 1152-1157
##[37]
B.-Y. Zhang, S.-Y. Xu, Y. Zou, Relaxed stability conditions for delayed recurrent neural networks with polytopic uncertainties, Int. J. Neural Syst., 16 (2006), 473-482
##[38]
J. Zhao, D. J. Hill, T. Liu, Global bounded synchronization of general dynamical networks with nonidentical nodes, IEEE Trans. Automat. Control, 57 (2012), 2656-2662
]
Fourier series of functions associated with higher-order Bernoulli polynomials
Fourier series of functions associated with higher-order Bernoulli polynomials
en
en
In this paper, we consider three types of functions associated with higher-order Bernoulli polynomials and derive their
Fourier series expansions. Further, we express each of them in term of Bernoulli functions.
2579
2591
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics, College of Natural Science
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Dmitry V.
Dolgy
Hrimwon
Kwangwoon University
Republic of Korea
dvdolgy@gmail.com
Jin-Woo
Park
Department of Mathematics Education
Daegu University
Republic of Korea
a0417001@knu.ac.kr
Fourier series
higher-order Bernoulli polynomials
Bernoulli functions.
Article.25.pdf
[
[1]
M. Abramowitz, I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, For sale by the Superintendent of Documents, U.S. Government Printing Office,, Washington, D.C. (1964)
##[2]
L. Carlitz, A note on Bernoulli numbers and polynomials, Elem. Math., 29 (1974), 90-92
##[3]
G. V. Dunne, C. Schubert, Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys., 7 (2013), 225-249
##[4]
C. Faber, R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math., 139 (2000), 173-199
##[5]
I. M. Gessel, On Miki’s identity for Bernoulli numbers, J. Number Theory, 110 (2005), 75-82
##[6]
H. W. Gould, Explicit formulas for Bernoulli numbers, Amer. Math. Monthly, 79 (1972), 44-51
##[7]
D. S. Kim, T. Kim, Bernoulli basis and the product of several Bernoulli polynomials, Int. J. Math. Math. Sci., 2012 (2012), 1-12
##[8]
D. S. Kim, T. Kim, A note on higher-order Bernoulli polynomials, J. Inequal. Appl., 2013 (2013), 1-9
##[9]
D. S. Kim, T. Kim, Some identities of higher order Euler polynomials arising from Euler basis, Integral Transforms Spec. Funct., 24 (2013), 734-738
##[10]
D. S. Kim, T. Kim, Higher-order Bernoulli and poly-Bernoulli mixed type polynomials, Georgian Math. J., 22 (2015), 265-272
##[11]
D. S. Kim, T. Kim, Fourier series of higher-order Euler functions and their applications, Bull. Korean Math. Soc., (to appear), -
##[12]
D. S. Kim, T. Kim, Y. H. Kim, S.-H. Lee , Some arithmetic properties of Bernoulli and Euler numbers, Adv. Stud. Contemp. Math. (Kyungshang), 22 (2012), 467-480
##[13]
T. Kim, D. S. Kim, S.-H. Rim, D. V. Dolgy, Fourier series of higher-order Bernoulli functions and their applications, J. Inequal. Appl., 2017 (2017), 1-7
##[14]
D. H. Lehmer, A new approach to Bernoulli polynomials, Amer. Math. Monthly, 95 (1988), 905-911
##[15]
J. E. Marsden, Elementary classical analysis, With the assistance of Michael Buchner, Amy Erickson, Adam Hausknecht, Dennis Heifetz, Janet Macrae and William Wilson, and with contributions by Paul Chernoff, István Fáry and Robert Gulliver, W. H. Freeman and Co., San Francisco (1974)
##[16]
K. Shiratani, S. Yokoyama , An application of p-adic convolutions, Mem. Fac. Sci. Kyushu Univ. Ser. A, 36 (1982), 73-83
##[17]
L. C. Washington, Introduction to cyclotomic fields, Second edition, Graduate Texts in Mathematics, Springer-Verlag, New York (1997)
##[18]
D. G. Zill, M. R. Cullen, Advanced engineering mathematics, Second edition, Jones and Bartlett Publishers, London, UK (2000)
]
Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters
Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters
en
en
In this paper, an adaptive control scheme is developed to study the add order synchronization and the add order antisynchronization
behavior between two different dimensional fractional order chaotic systems with fully uncertain parameters.
This design of adaptive controller is based on the Lyapunov stability theory. Analytic expression for the controller with its
adaptive laws of parameters is shown. The adaptive add order synchronization and add order anti-synchronization between
two fractional order chaotic systems are used to show the effectiveness of the proposed method. Theoretical analysis and
numerical simulations are used to verify the results.
2592
2606
M. M.
Al-sawalha
Mathematics Department, Faculty of Science
University of Hail
Kingdom of Saudi Arabia
sawalha_moh@yahoo.com
M.
Ghazel
Mathematics Department, Faculty of Science
University of Hail
Kingdom of Saudi Arabia
O. Y.
Ababneh
School of Mathematics
Zarqa University
Jordan
M.
Shoaib
Abu Dhabi Men’s College
Higher Colleges of Technology
United Arab Emirates
Add order
synchronization
anti-synchronization
adaptive control
unknown parameters
Lyapunov stability theory.
Article.26.pdf
[
[1]
S. K. Agrawal, S. Das, A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters, Nonlinear Dynam., 73 (2013), 907-919
##[2]
S. K. Agrawal, S. Das, Function projective synchronization between four dimensional chaotic systems with uncertain parameters using modified adaptive control method, J. Process Control, 24 (2014), 517-530
##[3]
S. K. Agrawal, M. Srivastava, S. Das, Synchronization of fractional order chaotic systems using active control method, Chaos Solitons Fractals, 45 (2012), 737-752
##[4]
I. Ahmad, A. B. Saaban, A. B. Ibrahim, M. Shahzad, N. Naveed, The synchronization of chaotic systems with different dimensions by a robust generalized active control, Optik, 127 (2016), 4859-4871
##[5]
M. M. Al-sawalha, A. Al-sawalha, Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control, Open Phys., 14 (2016), 304-313
##[6]
M. M. Al-sawalha, M. S. M. Noorani , Chaos reduced-order anti-synchronization of chaotic systems with fully unknown parameters, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1908-1920
##[7]
L. Y. T. Andrew, X.-F. Li, Y.-D. Chu, Z. Hui, A novel adaptive-impulsive synchronization of fractional-order chaotic systems, Chin. Phys. B, 24 (2015), 1-7
##[8]
D. Baleanu, G.-C. Wu, Y.-R. Bai, F.-L. Chen, Stability analysis of Caputo-like discrete fractional systems, Commun. Nonlinear Sci. Numer. Simul., 48 (2017), 520-530
##[9]
S. Bhalekar, V. Daftardar-Gejji , Synchronization of different fractional order chaotic systems using active control, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 3536-3546
##[10]
S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, C. S. Zhou, The synchronization of chaotic systems, Phys. Rep., 366 (2002), 1-101
##[11]
D.-Y. Chen, R.-F. Zhang, J. C. Sprott, H.-T. Chen, X.-Y. Ma, Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control, Chaos, 22 (2012), 1-9
##[12]
Z. Gao, X.-Z. Liao, Integral sliding mode control for fractional-order systems with mismatched uncertainties, Nonlinear Dynam., 72 (2013), 27-35
##[13]
F. Gao, X.-J. Yang, Local fractional Euler’s method for the steady heat-conduction problem, Therm. Sci., 20 (2016), 1-735
##[14]
A. K. Golmankhaneh, R. Arefi, D. Baleanu, Synchronization in a nonidentical fractional order of a proposed modified system, J. Vib. Control, 21 (2015), 1154-1161
##[15]
A. Hajipour, S. S. Aminabadi, Synchronization of chaotic Arneodo system of incommensurate fractional order with unknown parameters using adaptive method, Optik, 127 (2016), 7704-7709
##[16]
J.-H. He, A tutorial review on fractal spacetime and fractional calculus, Internat. J. Theoret. Phys., 53 (2014), 3698-3718
##[17]
R. Hilfer (Ed.), Applications of fractional calculus in physics, World Scientific Publishing Co., Inc., River Edge, NJ (2000)
##[18]
Y. Hu, J.-H. He, On fractal space-time and fractional calculus, Therm. Sci., 20 (2016), 773-777
##[19]
W. Jawaada, M. S. M. Noorani, M. M. Al-sawalha, Anti-synchronization of chaotic systems via adaptive sliding mode control, Chin. Phys. Lett., 29 (2012), 1-3
##[20]
W. Jawaada, M. S. M. Noorani, M. M. Al-sawalha, Robust active sliding mode anti-synchronization of hyperchaotic systems with uncertainties and external disturbances, Nonlinear Anal. Real World Appl., 13 (2012), 2403-2413
##[21]
A. M. Liapunov, Stability of motion, With a contribution by V. A. Pliss and an introduction by V. P. Basov, Translated from the Russian by Flavian Abramovici and Michael Shimshoni, Mathematics in Science and Engineering, Academic Press, New York-London (1966)
##[22]
F.-J. Liu, P. Wang, Y. Zhang, H.-Y. Liu, J.-H. He, A fractional model for insulation clothings with Cocoon-like porous structure, Therm. Sci., 20 (2016), 779-784
##[23]
W.-Y. Ma, C.-P. Li, Y.-J. Wu, Impulsive synchronization of fractional Takagi-Sugeno fuzzy complex networks, Chaos, 26 (2016), 1-8
##[24]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[25]
A. G. Radwan, K. Moaddy, K. N. Salama, S. Momani, I. Hashim, Control and switching synchronization of fractional order chaotic systems using active control technique, J. Adv. Res., 5 (2014), 125-132
##[26]
K. Sayevand, K. Pichaghchi, Analysis of nonlinear fractional KdV equation based on Hes fractional derivative, Nonlinear Sci. Lett. A, 7 (2016), 77-85
##[27]
X.-N. Song, S. Song, B. Li, Adaptive synchronization of two time-delayed fractional-order chaotic systems with different structure and different order, Optik, 127 (2016), 11860-11870
##[28]
D. Terman, N. Koppel, A. Bose, Dynamics of two mutually coupled slow inhibitory neurons, Phys. D, 117 (1998), 241-275
##[29]
Z. Wang, X. Huang, H. Shen, Control of an uncertain fractional order economic system via adaptive sliding mode, Neurocomputing, 83 (2012), 83-88
##[30]
K.-L. Wang, S.-Y. Liu, He’s fractional derivative for non-linear fractional Heat transfer equation, Therm. Sci., 20 (2016), 793-796
##[31]
S.Wang, Y.-G. Yu, M. Diao, Hybrid projective synchronization of chaotic fractional order systems with different dimensions, Phys. A, 389 (2010), 4981-4988
##[32]
G. C. Wu, D. Baleanu, Chaos synchronization of the discrete fractional logistic map, Signal Process., 102 (2014), 96-99
##[33]
G.-C. Wu, D. Baleanu, Discrete fractional logistic map and its chaos, Nonlinear Dynam., 75 (2014), 283-287
##[34]
G.-C. Wu, D. Baleanu, S.-D. Zeng, Discrete chaos in fractional sine and standard maps, Phys. Lett. A, 378 (2014), 484-487
##[35]
X.-J. Wu, Y. Lu, Generalized projective synchronization of the fractional-order Chen hyperchaotic system, Nonlinear. Dynam., 57 (2009), 25-35
##[36]
X.-J. Wu, H.-T. Lu, S.-L. Shen, Synchronization of a new fractional-order hyperchaotic system, Phys. Lett. A, 373 (2009), 2329-2337
##[37]
Y. Xu, H.Wang, D. Liu, H. Huang, Sliding mode control of a class of fractional chaotic systems in the presence of parameter perturbations, J. Vib. Control, 21 (2015), 435-448
##[38]
X.-J. Yang, H. M. Srivastava, D. F. M. Torres, Y.-D. Zhang, Non-differentiable solutions for local fractional nonlinear Riccati differential equations, Fund. Inform., 151 (2017), 409-417
##[39]
X.-J. Yang, J. A. Tenreiro Machado, J. J. Nieto, A new family of the local fractional PDEs, Fund. Inform., 151 (2017), 63-75
##[40]
G. Zhang, Z.-R. Liu, Z.-J. Ma, Generalized synchronization of different dimensional chaotic dynamical systems, Chaos Solitons Fractals, 32 (2007), 773-779
##[41]
P. Zhou, R.-J. Bai, The adaptive synchronization of fractional-order chaotic system with fractional-order 1 < q < 2 via linear parameter update law, Nonlinear Dynam., 80 (2015), 753-765
##[42]
M. Zribi, N. Smaoui, H. Salim, Synchronization of the unified chaotic systems using a sliding mode controller, Chaos Solitons Fractals, 42 (2009), 3197-3209
]
On the generalized fractional derivatives and their Caputo modification
On the generalized fractional derivatives and their Caputo modification
en
en
In this manuscript, we define the generalized fractional derivative on \(AC^n_\gamma
[a, b]\), the space of functions defined on [a, b]
such that
\(\gamma^{n-1}f\in AC[a, b]\), where
\(\gamma=x^{1-p}\frac{d}{dx}\). We present some of the properties of generalized fractional derivatives of these
functions and then we define their Caputo version.
2607
2619
F.
Jarad
Mathematics Department, Faculty of Arts and Sciences
ÇankayaUniversity
Turkey
fahd@cankaya.edu.tr
T.
Abdeljawad
Department of Mathematics and Physical Sciences
Prince Sultan University
Saudi Arabia
tabdeljawad@psu.edu.sa
D.
Baleanu
Mathematics Department, Faculty of Arts and Sciences
Institute of Space Sciences
ÇankayaUniversity
Turkey
Romania
dumitru@cankaya.edu.tr
Riemann-Liouville fractional derivatives
Caputo fractional derivatives
Hadamard fractional derivatives
Caputo-Hadamard fractional derivatives
generalized fractional integral
generalized Caputo fractional derivatives.
Article.27.pdf
[
[1]
T. Abdeljawad, Dual identities in fractional difference calculus within Riemann, Adv. Difference Equ., 2013 (2013), 1-16
##[2]
T. Abdeljawad, On delta and nabla Caputo fractional differences and dual identities, Discrete Dyn. Nat. Soc., 2013 (2013), 1-12
##[3]
T. Abdeljawad, D. Baleanu, Fractional differences and integration by parts, J. Comput. Anal. Appl., 13 (2011), 574-582
##[4]
T. Abdeljawad, D. Baleanu, Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels, Adv. Difference Equ., 2016 (2016), 1-18
##[5]
R. Almeida, A. B. Malinowska, T. Odzijewicz, Fractional differential equations with dependence on the Caputo- Katugampola derivative, J. Comput. Nonlinear Dyn., 11 (2016), 1-11
##[6]
F. M. Atıcı, S. Şengül, Modeling with fractional difference equations, J. Math. Anal. Appl., 369 (2010), 1-9
##[7]
M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 73-85
##[8]
Y. Y. Gambo F. Jarad, D. Baleanu, T. Abdeljawad, On Caputo modification of the Hadamard fractional derivatives, Adv. Difference Equ., 2014 (2014), 1-12
##[9]
F. Gao, X.-J. Yang, Fractional Maxwell fluid with fractional derivative without singular kernel, Therm. Sci., 20 (2016), 1-871
##[10]
C. Goodrich, A. C. Peterson, Discrete fractional calculus, Springer, Cham (2015)
##[11]
R. Hilfer (Ed.), Applications of fractional calculus in physics, World Scientific Publishing Co., Inc., River Edge, NJ (2000)
##[12]
F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Adv. Difference Equ., 2012 (2012), 1-8
##[13]
U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., 218 (2011), 860-865
##[14]
U. N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6 (2014), 1-15
##[15]
A. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc., 38 (2001), 1191-1204
##[16]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[17]
J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 87-92
##[18]
J. T. Machado, V. Kiryakova, F. Mainardi, Recent history of fractional calculus, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 1140-1153
##[19]
R. L. Magin, Fractional calculus in bioengineering, Begell House Publishers, CT (2006)
##[20]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[21]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Theory and applications, Edited and with a foreword by S. M. Nikolski˘ı, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon (1993)
##[22]
X.-J. Yang, D. Baleanu, H. M. Srivastava, Local fractional integral transforms and their applications, Elsevier/Academic Press, Amsterdam (2016)
##[23]
X.-J. Yang, F. Gao, J. A. Tenreiro Machado, D. Baleanu, A new fractional derivative involving the normalized sinc function without singular kernel, ArXiv, 2017 (2017), 1-11
]
Solving fuzzy fractional differential equations using fuzzy Sumudu transform
Solving fuzzy fractional differential equations using fuzzy Sumudu transform
en
en
In this paper, we apply fuzzy Sumudu transform (FST) for solving linear fuzzy fractional differential equations (FFDEs)
involving Caputo fuzzy fractional derivative. It is followed by suggesting a new result on the property of FST for Caputo fuzzy
fractional derivative. We then construct a detailed procedure on finding the solutions of linear FFDEs and finally, we demonstrate
a numerical example.
2620
2632
Norazrizal Aswad Abdul
Rahman
Institute of Engineering Mathematics
Universiti Malaysia Perlis
Malaysia
norazrizalaswad@gmail.com
Muhammad Zaini
Ahmad
Institute of Engineering Mathematics
Universiti Malaysia Perlis
Malaysia
mzaini@unimap.edu.my
Caputo fuzzy fractional derivative
fuzzy Sumudu transform
fuzzy fractional differential equation.
Article.28.pdf
[
[1]
N. A. Abdul Rahman, M. Z. Ahmad, Applications of the fuzzy Sumudu transform for the solution of first order fuzzy differential equations, Entropy, 17 (2015), 4582-4601
##[2]
O. P. Agrawal, Solution for a fractional diffusion-wave equation defined in a bounded domain, Fractional order calculus and its applications, Nonlinear Dynam., 29 (2002), 145-155
##[3]
R. P. Agarwal, V. Lakshmikantham, J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72 (2010), 2859-2862
##[4]
M. Z. Ahmad, N. A. Abdul Rahman, Explicit solution of fuzzy differential equations by mean of fuzzy Sumudu transform, Int. J. Appl. Phys. Math., 5 (2015), 86-93
##[5]
M. Z. Ahmad, M. K. Hasan, S. Abbasbandy, Solving fuzzy fractional differential equations using Zadeh’s extension principle, Scientific World J., 2013 (2013), 1-11
##[6]
A. Ahmadian, M. Suleiman, S. Salahshour, D. Baleanu, A Jacobi operational matrix for solving a fuzzy linear fractional differential equation, Adv. Difference Equ., 2013 (2013), 1-29
##[7]
T. Allahviranloo, M. B. Ahmadi, Fuzzy Laplace transforms, Soft Comput., 14 (2010), 235-243
##[8]
T. Allahviranloo, A. Armand, Z. Gouyandeh, Fuzzy fractional differential equations under generalized fuzzy Caputo derivative, J. Intell. Fuzzy Systems, 26 (2014), 1481-1490
##[9]
T. Allahviranloo, S. Salahshour, S. Abbasbandy, Explicit solutions of fractional differential equations with uncertainty, Soft Comput., 16 (2012), 297-302
##[10]
S. Arshad, V. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Anal., 74 (2011), 3685-3693
##[11]
B. Bede, S. G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Sets and Systems, 147 (2004), 385-403
##[12]
B. Bede, S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 (2005), 581-599
##[13]
B. Bede, I. J. Rudas, A. L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Inform. Sci., 177 (2007), 1648-1662
##[14]
D. A. Benson, S. W. Wheatcraft, M. M. Meerschaert, Application of a fractional advection-dispersion equation, Water Resour. Res., 36 (2000), 1403-1412
##[15]
A. H. Bhrawy, M. A. Zaky, Shifted fractional-order Jacobi orthogonal functions: application to a system of fractional differential equations, Appl. Math. Model., 40 (2016), 832-845
##[16]
H. Bulut, H. M. Baskonus, F. B. M. Belgacem, The analytical solution of some fractional ordinary differential equations by the Sumudu transform method, Abstr. Appl. Anal., 2013 (2013), 1-6
##[17]
F. Bulut, Ö. Oruç, A. Esen, Numerical Solutions of Fractional System of Partial Differential Equations By Haar Wavelets, Comput. Model. Eng. Sci., 108 (2015), 263-284
##[18]
V. B. L. Chaurasia, R. S. Dubey, F. B. M. Belgacem, Fractional radial diffusion equation analytical solution via Hankel and Sumudu transforms, Int. J. Math. Eng. Sci. Aero., 3 (2012), 179-188
##[19]
V. B. L. Chaurasia, J. Singh, Application of Sumudu transform in Schödinger equation occurring in quantum mechanics , Appl. Math. Sci. (Ruse), 4 (2010), 2843-2850
##[20]
M. Friedman, M. Ma, A. Kandel, Numerical solutions of fuzzy differential and integral equations, Fuzzy modeling and dynamics, Fuzzy Sets and Systems, 106 (1999), 35-48
##[21]
V. Garg, K. Singh, An improved Grunwald-Letnikov fractional differential mask for image texture enhancement, Int. J. Adv. Comput. Sci. Appl., 3 (2012), 130-135
##[22]
W. G. Glöckle, T. F. Nonnenmacher, A fractional calculus approach to self-similar protein dynamics, Biophys. J., 68 (1995), 46-53
##[23]
A. K. Haydar, Fuzzy Sumudu transform for fuzzy nth-order derivative and solving fuzzy ordinary differential equations, Int. J. Sci. Res., 4 (2015), 1372-1378
##[24]
F. Jarad, K. Tas, Application of Sumudu and double Sumudu transforms to Caputo-fractional differential equations, J. Comput. Anal. Appl., 14 (2012), 475-483
##[25]
G. Jumarie, Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution, J. Appl. Math. Comput., 24 (2007), 31-48
##[26]
O. Kaleva, A note on fuzzy differential equations, Nonlinear Anal., 64 (2006), 895-900
##[27]
Q. D. Katatbeh, F. B. M. Belgacem, Applications of the Sumudu transform to fractional differential equations, Nonlinear Stud., 18 (2011), 99-112
##[28]
A. Kaufmann, M. M. Gupta, Introduction to fuzzy arithmetic, With a foreword by Lotfi A. Zadeh, Van Nostrand Reinhold Electrical/Computer Science and Engineering Series, Van Nostrand Reinhold Co., New York (1985)
##[29]
A. Khastan, J. J. Nieto, R. Rodríguez-López, Variation of constant formula for first order fuzzy differential equations, Fuzzy Sets and Systems, 177 (2011), 20-33
##[30]
A. A. Kilbas, S. A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, (Russian); translated from Differ. Uravn., 41 (2005), 82–86, Differ. Equ., 41 (2005), 84-89
##[31]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[32]
J. W. Layman, The Hankel transform and some of its properties, J. Integer Seq., 4 (2001), 1-11
##[33]
V. Lupulescu, Fractional calculus for interval-valued functions, Fuzzy Sets and Systems, 265 (2015), 63-85
##[34]
M. Ma, M. Friedman, A. Kandel, Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems, 105 (1999), 133-138
##[35]
F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Appl. Math. Lett., 9 (1996), 23-28
##[36]
M. Mazandarani, A. V. Kamyad, Modified fractional Euler method for solving fuzzy fractional initial value problem, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 12-21
##[37]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[38]
S. Salahshour, T. Allahviranloo, S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1372-1381
##[39]
E. Sousa, C. Li , A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative, Appl. Numer. Math., 90 (2015), 22-37
##[40]
R. A. Spinelli, Numerical inversion of a Laplace transform, SIAM J. Numer. Anal., 3 (1966), 636-649
##[41]
L. Stefanini, L. Sorini, M. L. Guerra, Parametric representation of fuzzy numbers and application to fuzzy calculus, Fuzzy Sets and Systems, 157 (2006), 2423-2455
##[42]
M. Stynes, J. L. Gracia, A finite difference method for a two-point boundary value problem with a Caputo fractional derivative, IMA J. Numer. Anal., 35 (2015), 698-721
##[43]
D. Takači, A. Takači, A. Takači, On the operational solutions of fuzzy fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 1100-1113
##[44]
C. J. Tranter, The use of the Mellin transform in finding the stress distribution in an infinite wedge, Quart. J. Mech. Appl. Math. , 1 (1948), 125-130
##[45]
G. K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Internat. J. Math. Ed. Sci. Tech., 24 (1993), 35-43
##[46]
H.-C. Wu, The improper fuzzy Riemann integral and its numerical integration, Inform. Sci., 111 (1998), 109-137
##[47]
J.-P. Xu, Z.-G. Liao, Z.-N. Hu, A class of linear differential dynamical systems with fuzzy initial condition, Fuzzy Sets and Systems, 158 (2007), 2339-2358
##[48]
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353
]
Approximation of the mixed additive and cubic functional equation in paranormed spaces
Approximation of the mixed additive and cubic functional equation in paranormed spaces
en
en
In this paper, we prove some theorems about the Hyers-Ulam stability of the functional equation
\[f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 2[f(2x) - 2f(x)]\]
in paranormed spaces. From these theorems, as corollaries, we obtain the stability of the above functional equation with weaker
conditions controlled by product of powers of norms and mixed-type product-sum of powers of norms.
2633
2641
Zhihua
Wang
School of Science
Hubei University of Technology
P. R. China
matwzh2000@126.com
Prasanna K.
Sahoo
Department of Mathematics
University of Louisville
USA
sahoo@louisville.edu
Additive map
cubic map
Hyers-Ulam stability
paranormed space.
Article.29.pdf
[
[1]
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[2]
G. L. Forti, The stability of homomorphisms and amenability, with applications to functional equations, Abh. Math. Sem. Univ. Hamburg, 57 (1987), 215-226
##[3]
P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
##[4]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27 (1941), 222-224
##[5]
D. H. Hyers, G. Isac, T. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Boston, Inc., Boston, MA (1998)
##[6]
S.-M. Jung, Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, Springer Optimization and Its Applications, Springer, New York (2011)
##[7]
P. Kannappan, Functional equations and inequalities with applications, Springer Monographs in Mathematics, Springer, New York (2009)
##[8]
S. Lee, C. Park, J. R. Lee, Functional inequalities in paranormed spaces, J. Chungcheong Math. Soc., 26 (2013), 287-296
##[9]
A. Najati, G. Z. Eskandani, Stability of a mixed additive and cubic functional equation in quasi-Banach spaces, J. Math. Anal. Appl., 342 (2008), 1318-1331
##[10]
C. Park, Stability of an AQCQ-functional equation in paranormed spaces, Adv. Difference Equ., 2012 (2012), 1-20
##[11]
C. Park, J. R. Lee, An AQCQ-functional equation in paranormed spaces, Adv. Difference Equ., 2012 (2012), 1-9
##[12]
C. Park, J. R. Lee, Functional equations and inequalities in paranormed spaces, J. Inequal. Appl., 2013 (2013), 1-23
##[13]
C. Park, D. Y. Shin, Functional equations in paranormed spaces, Adv. Difference Equ., 2012 (2012), 1-14
##[14]
T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
##[15]
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal., 46 (1982), 126-130
##[16]
T. M. Rassias (Ed.), Functional equations, inequalities and applications, Kluwer Academic Publishers, Dordrecht (2003)
##[17]
P. K. Sahoo, P. Kannappan, Introduction to functional equations, CRC Press, Boca Raton, FL (2011)
##[18]
S. M. Ulam, Problems in modern mathematics, Science Editions John Wiley & Sons, Inc., New York (1964)
]
New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation
New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation
en
en
Exact homoclinic breather wave solution for the coupled Schrödinger -Boussinesq equation is obtained by using homoclinic
test technique. Based on the homoclinic breather wave solution, rational homoclinic breather wave solution is generated by
homoclinic breather limit method, rogue wave in the form of the rational homoclinic solution is derived when the period
of homoclinic breather wave goes to infinite. This is a new way for generating rogue wave which is different from direct
constructing method, Darboux dressing technique and ansätz with complexity of parameter. This result shows the homoclinic
rogue wave can be generated from homoclinic breather wave, and it is useful for explaining some related nonlinear phenomenon.
2642
2648
Longxing
Li
College of Mathematics and Statistics
Qujing Normal University
P. R. China
llxyz891008@163.com
Zhengde
Dai
School of Mathematics and Statistics
Yunnan University
P. R. China
zhddai@ynu.edu.cn
Schrödinger -Boussinesq equation
Hirota bilinear form
homoclinic breather limit method
rogue wave.
Article.30.pdf
[
[1]
M. J. Ablowitz, P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering , London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (1991)
##[2]
N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, Rogue waves and rational solutions of the nonlinear Schrödinger equation, Phys. Rev. E., 80 (2009), 1-9
##[3]
U. Bandelow, N. Akhmediev, Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa- Satsuma case, Phys. Lett. A., 367 (2012), 1558-1561
##[4]
Y. V. Bludov, V. V. Konotop, N. Akhmediev, Matter rogue waves, Phys. Rev. A., 80 (2009), 1-5
##[5]
Y. V. Bludov, V. V. Konotop, N. Akhmediev, Vector rogue waves in binary mixtures of Bose-Einstein condensates, Eur. Phys. J. Spec. Top., 185 (2010), 169-180
##[6]
A. R. Chowdhury, B. Dasgupta, N. N. Rao, Painlevé analysis and Backlund transformations for coupled generalized Schrödinger -Boussinesq system, Chaos Solitons Fractals, 9 (1998), 1747-1753
##[7]
K. Dysthe, H. E. Krogstad, P. Müller, Oceanic rogue waves, Annual review of fluid mechanics, Annu. Rev. Fluid Mech., Annual Reviews, Palo Alto, CA, 40 (2008), 287-310
##[8]
A. N. Ganshin, V. B. Efimov, G. V. Kolmakov, L. P. Mezhov-Deglin, P. V. McClintock, Observation of an inverse energy cascade in developed acoustic turbulence in superfluid helium, Phys. Rev. lett., 101 (2008), 1-4
##[9]
Y. Hase, J. Satsuma, An N-soliton solution for the nonlinear Schrödinger equation coupled to the Boussinesq equation, J. Phys. Soc. Japan, 57 (1988), 679-682
##[10]
X.-B. Hu, B.-L. Guo, H.-W. Tan, Homoclinic orbits for the coupled Schrödinger -Boussinesq equation and coupled Higgs equation, J. Phys. Soc. Japan, 72 (2003), 189-190
##[11]
M.-R. Jiang, Z.-D. Dai, Various heteroclinic solutions for the coupled Schrödinger -Boussinesq equation, Abstr. Appl. Anal., 2013 (2013), 1-5
##[12]
C. Kharif, E. Pelinovsky, A. Slunyaev, Rogue waves in the ocean, Advances in Geophysical and Environmental Mechanics and Mathematics, Springer-Verlag, Berlin (2009)
##[13]
C.-Z. Li, J.-S. He, K. Porseizan, Rogue waves of the Hirota and the Maxwell-Bloch equations, Phys. Rev. E, 87 (2013), 1-13
##[14]
A. Montina, U. Bortolozzo, S. Residori, F. T. Arecchi, Non-Gaussian statistics and extreme waves in a nonlinear optical cavity, Phys. Rev. Lett., 103 (2009), 1-4
##[15]
G. Mu, Z.-Y. Qin, Rogue waves for the coupled Schrödinger -Boussinesq equation and the coupled Higgs equation, J. Phys. Soc. Japan, 81 (2012), 1-6
##[16]
Y. Ohta, J.-K. Yang, Dynamics of rogue waves in the Davey-Stewartson II equation, J. Phys. A, 46 (2013), 1-19
##[17]
D. H. Peregrine, Water waves, nonlinear Schrödinger equations and their solutions, J. Austral. Math. Soc. Ser. B, 25 (1983), 16-43
##[18]
N. N. Rao, P. K. Shukla, Coupled Langmuir and ion-acoustic waves in two-electron temperature plasmas, Phys. Plasmas, 4 (1997), 636-645
##[19]
P. Saha, S. Banerjee, A. R. Chowdhury, Normal form analysis and chaotic scenario in a Schrödinger -Boussinesq system, Chaos Solitons Fractals, 14 (2002), 145-153
##[20]
N. L. Shatashvili, N. N. Rao, Localized nonlinear structures of intense electromagnetic waves in two-electron-temperature electron-positron-ion plasmas, Phys. Plasmas, 6 (1999), 66-71
##[21]
D. R. Solli, C. Ropers, P. Koonath, B. Jalali, Optical rogue waves, Nature, 450 (2007), 1054-1057
##[22]
Y.-S. Tao, J.-S. He, Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation, Phys. Rev. E, 85 (2012), 1-7
##[23]
C.-J. Wang, Z.-D. Dai, Various breathers and rogue waves for the coupled long-wave-short-wave system, Adv. Difference Equ., 87 (2014), 1-10
##[24]
C.-J. Wang, Z.-D. Dai, C.-F. Liu, From a breather homoclinic wave to a rogue wave solution for the coupled Schrödinger - Boussinesq equation, Phys. Scripta, 89 (2014), 1-10
##[25]
Z.-Y. Yan, Financial rogue waves, Commun. Theor. Phys., 54 (2010), 947-949
##[26]
X.-J. Yang, A new integral transform operator for solving the heat-diffusion problem, Appl. Math. Lett., 64 (2017), 193-197
##[27]
X.-J. Yang, D. Baleanu, Y. Khan, S. T. Mohyud-Din, Local fractional variational iteration method for diffusion and wave equations on Cantor sets, Romanian J. Phys., 59 (2014), 36-48
##[28]
X.-J. Yang, F. Gao, A new technology for solving diffusion and heat equations, Therm. Sci., 21 (2017), 133-140
##[29]
X.-J. Yang, F. Gao, H. M. Srivastava, Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations, Comput. Math. Appl., 73 (2017), 203-210
##[30]
L.-C. Zhao, J. Liu, Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation, Phys. Rev. E., 87 (2013), 1-8
##[31]
W.-P. Zhong, Rogue wave solutions of the generalized one-dimensional Gross-Pitaevskii equation, J. Nonlinear Opt. Phys. Mater., 21 (2012), 1-9
]
The split variational inequality problem and its algorithm iteration
The split variational inequality problem and its algorithm iteration
en
en
The split variational inequality problem under a nonlinear transformation has been considered. An iterative algorithm is
presented to solve this split problem. Strong convergence results are obtained.
2649
2661
Yonghong
Yao
Department of Mathematics
Tianjin Polytechnic University
China
yaoyonghong@aliyun.com
Xiaoxue
Zheng
Department of Mathematics
Tianjin Polytechnic University
China
zhengxiaoxue1991@aliyun.com
Limin
Leng
Department of Mathematics
Tianjin Polytechnic University
China
lenglimin@aliyun.com
Shin Min
Kang
Center for General Education
Department of Mathematics and the RINS
China Medical University
Gyeongsang National University
Taiwan
Korea
smkang@gnu.ac.kr
Split variational inequality
iterative algorithm
nonlinear transformation.
Article.31.pdf
[
[1]
M. Aslam Noor, Some developments in general variational inequalities, Appl. Math. Comput., 152 (2004), 199-277
##[2]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
##[3]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, An extragradient method for solving split feasibility and fixed point problems, Comput. Math. Appl., 64 (2012), 633-642
##[4]
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
##[5]
L.-C. Ceng, M. Teboulle, J.-C. Yao, Weak convergence of an iterative method for pseudomonotone variational inequalities and fixed-point problems, J. Optim. Theory Appl., 146 (2010), 19-31
##[6]
L.-C. Ceng, J.-C. Yao, Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems, Taiwanese J. Math., 10 (2006), 1293-1303
##[7]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353-2365
##[8]
Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
##[9]
Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084
##[10]
Y. Censor, A. Gibali, S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms, 59 (2012), 301-323
##[11]
Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587-600
##[12]
F. Cianciaruso, G. Marino, L. Muglia, Y.-H. Yao, On a two-step algorithm for hierarchical fixed point problems and variational inequalities, J. Inequal. Appl., 2009 (2009), 1-13
##[13]
R. Glowinski, Numerical methods for nonlinear variational problems, Springer Series in Computational Physics, Springer-Verlag, New York (1984)
##[14]
Z.-H. He, W.-S. Du, On hybrid split problem and its nonlinear algorithms, Fixed Point Theory Appl., 2013 (2013), 1-20
##[15]
Z.-H. He, W.-S. Du, On split common solution problems: new nonlinear feasible algorithms, strong convergence results and their applications, Fixed Point Theory Appl., 2014 (2014), 1-16
##[16]
A. N. Iusem, An iterative algorithm for the variational inequality problem, Mat. Apl. Comput., 13 (1994), 103-114
##[17]
G. M. Korpelevič, An extragradient method for finding saddle points and for other problems, (Russian) ´Ekonom. i Mat. Metody, 12 (1976), 747-756
##[18]
P. E. Mainge, Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325 (2007), 469-479
##[19]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488-502
##[20]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 1-9
##[21]
R.-T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optimization, 14 (1976), 877-898
##[22]
W. Takahashi, M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., 118 (2003), 417-428
##[23]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 2 (2002), 240-256
##[24]
H.-K. Xu, A variable Krasnoselski˘ı-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22 (2006), 2021-2034
##[25]
H.-K. Xu, Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Problems, 26 (2010), 1-17
##[26]
Y.-H. Yao, R. P. Agarwal, M. Postolache, Y.-C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., 183 (2014), 1-14
##[27]
Y.-H. Yao, R.-D. Chen, H.-K. Xu, Schemes for finding minimum-norm solutions of variational inequalities, Nonlinear Anal., 72 (2010), 3447-3456
##[28]
Y.-H. Yao, W. Jigang, Y.-C. Liou, Regularized methods for the split feasibility problem, Abstr. Appl. Anal., 2012 (2012), 1-13
##[29]
Y.-H. Yao, Y.-C. Liou, S. M. Kang, Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method, Comput. Math. Appl., 59 (2010), 3472-3480
##[30]
Y.-H. Yao, Y.-C. Liou, J.-C. Yao, Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction, Fixed Point Theory Appl., 2015 (2015), 1-19
##[31]
Y.-H. Yao, M. A. Noor, Y.-C. Liou, Strong convergence of a modified extragradient method to the minimum-norm solution of variational inequalities, Abstr. Appl. Anal., 2012 (2012), 1-9
##[32]
Y.-H. Yao, M. A. Noor, Y.-C. Liou, S. M. Kang, Iterative algorithms for general multivalued variational inequalities, Abstr. Appl. Anal., 2012 (2012), 1-10
##[33]
Y.-H. Yao, M. Postolache, Y.-C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory Appl., 2013 (2013), 1-12
##[34]
H. Zegeye, N. Shahzad, Y.-H. Yao, Minimum-norm solution of variational inequality and fixed point problem in Banach spaces, Optimization, 64 (2015), 453-471
##[35]
L. J. Zhang, J. M. Chen, Z. B. Hou, Viscosity approximation methods for nonexpansive mappings and generalized variational inequalities, (Chinese) Acta Math. Sinica (Chin. Ser.), 53 (2010), 691-698
]
New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces
New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces
en
en
In this paper, we introduce the notions of \(\theta-\phi\) contraction and \(\theta-\phi\) Suzuki contraction and establish some new fixed point
theorems for these mappings in the setting of complete metric spaces. The results presented in the paper improve and extend
the corresponding results due to Banach, Browder [F. E. Browder, Nederl. Akad. Wetensch. Proc. Ser. A Indag. Math., 30
(1968), 27–35], Suzuiki [T. Suzuki, Nonlinear Anal., 71 (2009), 5313–5317], Kannan [R. Kannan, Amer. Math. Monthly, 76 (1969),
405–408], Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages]. Finally, we give an example to illustrate
them.
2662
2670
Dingwei
Zheng
College of Mathematics and Information Science
Guangxi University
P. R. China
dwzheng@gxu.edu.cn
Zhangyong
Cai
Department of Mathematics
Guangxi Teachers Education University
P. R. China
zycaigxu2002@126.com
Pei
Wang
School of Mathematics and Information Science
Yulin Normal University
P. R. China
274958670@qq.com
Fixed point
complete metric space
\(\theta-\phi\) contraction.
Article.32.pdf
[
[1]
F. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901
##[2]
D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458-464
##[3]
F. E. Browder, On the convergence of successive approximations for nonlinear functional equations, Nederl. Akad. Wetensch. Proc. Ser. A Indag. Math., 30 (1968), 27-35
##[4]
J. Dugundji, A. Granas, Weakly contractive maps and elementary domain invariance theorem, Bull. Soc. Math. Gréce (N.S.), 19 (1978), 141-151
##[5]
J. R. Jachymski, Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., 125 (1997), 2327-2335
##[6]
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
##[7]
R. Kannan, Some results on fixed points, II , Amer. Math. Monthly, 76 (1969), 405-408
##[8]
J. Matkowski, Integrable solutions of functional equations, Dissertationes Math. (Rozprawy Mat.), 127 (1975), 1-68
##[9]
H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
##[10]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi-\)contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[11]
T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317
##[12]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-6
]
Continuous dependence of semilinear Petrovsky equation
Continuous dependence of semilinear Petrovsky equation
en
en
In this study, we obtain the continuous dependence on the coefficients of solutions of semilinear Petrovsky equation. Such
models are involved in various fields of mathematical physics likewise geophysical and oceanic applications.
2671
2677
Hüseyin
Kocaman
Department of Mathematics
Sakarya University
Turkey
Metin
Yaman
Department of Mathematics
Sakarya University
Turkey
myaman@sakarya.edu.tr
Şevket
Gür
Department of Mathematics
Sakarya University
Turkey
Semilinear Petrovsky equation
continuous dependence.
Article.33.pdf
[
[1]
G. N. Aliyeva, V. K. Kalantarov, Structural stability for FitzHugh-Nagumo equations, Appl. Comput. Math., 10 (2011), 289-293
##[2]
N. E. Amroun, A. Benaissa, Global existence and energy decay of solutions to a Petrovsky equation with general nonlinear dissipation and source term, Georgian Math. J., 13 (2006), 397-410
##[3]
A. O. Çelebi, V. K. Kalantarov, D. Uğurlu, Structural stability for the double diffusive convective Brinkman equations, Appl. Anal., 87 (2008), 933-942
##[4]
A.O. Çelebi, K. Gür, V. K. Kalantarov , Structural stability and decay estimate for marine riser equations, Math. Comput. Modelling, 54 (2011), 3182-3188
##[5]
J. Chen, Y. Jin, Continuous dependence on a parameter for classical solutions to first-order quasilinear hyperbolic systems, (Chinese) J. Fudan Univ. Nat. Sci., 39 (2000), 506-513
##[6]
W.-Y. Chen, Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal., 70 (2009), 3203-3208
##[7]
M. G. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein, S. Romanelli, Continuous dependence in hyperbolic problems with Wentzell boundary conditions, Commun. Pure Appl. Anal., 13 (2014), 419-433
##[8]
X.-S. Han, M.-X. Wang, Asymptotic behavior for Petrovsky equation with localized damping, Acta Appl. Math., 110 (2010), 1057-1076
##[9]
E. S. Huseynova, On behaviour of solution of Cauchy’s problem for one correct by Petrovsky equation at large time values, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., Math. Mech., 26 (2006), 85-96
##[10]
B. A. Iskenderov, E. S. Huseynova, Estimation of the solution to Cauchy problem for a correct by Petrovsky equation, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., Math. Mech., 29 (2009), 61-70
##[11]
G. Li, Y. Sun, W.-J. Liu, Global existence, uniform decay and blow-up of solutions for a system of Petrovsky equations, Nonlinear Anal., 74 (2011), 1523-1538
##[12]
A. V. Perjan, The continuous dependence of solutions of hyperbolic equations on initial data and coefficients, Studia Univ. Babeş-Bolyai Math., 37 (1992), 87-111
##[13]
F. Tahamtani, A. Peyravi, Global existence, uniform decay, and exponential growth of solutions for a system of viscoelastic Petrovsky equations, Turkish J. Math., 38 (2014), 87-109
##[14]
F. Tahamtani, M. Shahrouzi, Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term, Bound. Value Probl., 2012 (2012), 1-15
##[15]
M. Yaman, Ş. Gür, Continuous dependence for the damped nonlinear hyperbolic equation, Math. Comput. Appl., 16 (2011), 437-442
##[16]
Y. C. You, Energy decay and exact controllability for the Petrovsky equation in a bounded domain, Adv. in Appl. Math., 11 (1990), 372-388
##[17]
Y. C. You, Boundary stabilization of two-dimensional Petrovsky equation: vibrating plate, Differential Integral Equations, 4 (1991), 617-638
]
Semicontinuity of approximate solution mappings for parametric generalized weak vector equilibrium problems
Semicontinuity of approximate solution mappings for parametric generalized weak vector equilibrium problems
en
en
In this paper, we first introduce a new set-valued mapping by the scalar approximate solution mapping of a parametric
generalized weak vector equilibrium problem and obtain some of its properties. By one of obtained properties, we establish the
lower semicontinuity the approximate solution mapping to a parametric generalized weak vector equilibrium problem without
the assumptions about monotonicity and approximate solution mappings. Simultaneously, under some suitable conditions, we
obtain the upper semicontinuity of the approximate solution mapping to a generalized parametric weak vector equilibrium
problem. Our main results improve and extend the corresponding ones in the literature.
2678
2688
Qilin
Wang
College of Mathematics and Statistics
Chongqing Jiaotong University
China
wangql97@126.com
Xiaobing
Li
College of Mathematics and Statistics
Chongqing Jiaotong University
China
xiaobinglicq@126.com
Jing
Zeng
College of Mathematics and Statistics
Chongqing Technology and Business University
China
yiyuexue219@163.com
Parametric generalized weak vector equilibrium problems
lower semicontinuity
upper semicontinuity
approximate solution mappings.
Article.34.pdf
[
[1]
L. Q. Anh, P. Q. Khanh, Semicontinuity of the approximate solution sets of multivalued quasiequilibrium problems, Numer. Funct. Anal. Optim., 29 (2008), 24-42
##[2]
J. P. Aubin, I. Ekeland, Applied nonlinear analysis, Pure and Applied Mathematics (New York), AWiley-Interscience Publication, John Wiley & Sons, Inc., New York (1984)
##[3]
C. Berge, Topological spaces, Including a treatment of multi-valued functions, vector spaces and convexity, Translated from the French original by E. M. Patterson, Reprint of the 1963 translation, Dover Publications, Inc., Mineola, NY (1963)
##[4]
J. Borwein, Multivalued convexity and optimization: a unified approach to inequality and equality constraints, Math. Programming, 13 (1977), 183-199
##[5]
B. Chen, N.-J. Huang, Continuity of the solution mapping to parametric generalized vector equilibrium problems, J. Global Optim., 56 (2013), 1515-1528
##[6]
C. R. Chen, S. J. Li, On the solution continuity of parametric generalized systems, Pac. J. Optim., 6 (2010), 141-151
##[7]
C. R. Chen, S. J. Li, K. L. Teo, Solution semicontinuity of parametric generalized vector equilibrium problems, J. Global Optim., 45 (2009), 309-318
##[8]
Y. H. Cheng, D. L. Zhu, Global stability results for the weak vector variational inequality, J. Global Optim., 32 (2005), 543-550
##[9]
C. Chiang, O. Chadli, J.-C. Yao, Generalized vector equilibrium problems with trifunctions, J. Global Optim., 30 (2004), 135-154
##[10]
A. P. Farajzadeh, M. Mursaleen, A. Shafie, On mixed vector equilibrium problems, Azerb. J. Math., 6 (2016), 87-102
##[11]
J.-Y. Fu, Generalized vector quasi-equilibrium problems, Math. Methods Oper. Res., 52 (2000), 57-64
##[12]
J.-Y. Fu, Vector equilibrium problems. Existence theorems and convexity of solution set, J. Global Optim., 31 (2005), 109-119
##[13]
F. Giannessi (Ed.), Vector variational inequalities and vector equilibria, Mathematical theories, Nonconvex Optimization and its Applications, Kluwer Academic Publishers, Dordrecht (2000)
##[14]
X. H. Gong, Continuity of the solution set to parametric weak vector equilibrium problems, J. Optim. Theory Appl., 139 (2008), 35-46
##[15]
X. H. Gong, J. C. Yao, Lower semicontinuity of the set of efficient solutions for generalized systems, J. Optim. Theory Appl., 138 (2008), 197-205
##[16]
A. Göpfert, H. Riahi, C. Tammer, C. Zălinescu, Variational methods in partially ordered spaces, CMS Books in Mathematics/ Ouvrages de Mathmatiques de la SMC, Springer-Verlag, New York (2003)
##[17]
Y. Han, X.-H. Gong, Lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems, Appl. Math. Lett., 28 (2014), 38-41
##[18]
P. Q. Khanh, L. M. Luu, Lower semicontinuity and upper semicontinuity of the solution sets and approximate solution sets of parametric multivalued quasivariational inequalities, J. Optim. Theory Appl., 133 (2007), 329-339
##[19]
K. Kimura, J.-C. Yao, Semicontinuity of solution mappings of parametric generalized vector equilibrium problems, J. Optim. Theory Appl., 138 (2008), 429-443
##[20]
Z.-F. Li, G.-Y. Chen, Lagrangian multipliers, saddle points, and duality in vector optimization of set-valued maps, J. Math. Anal. Appl., 215 (1997), 297-316
##[21]
S. J. Li, Z. M. Fang, Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality, J. Optim. Theory Appl., 147 (2010), 507-515
##[22]
X. B. Li, S. J. Li, Continuity of approximate solution mappings for parametric equilibrium problems, J. Global Optim., 51 (2011), 541-548
##[23]
X. B. Li, S. J. Li, C. R. Chen, Lipschitz continuity of an approximate solution mapping to equilibrium problems, Taiwanese J. Math., 16 (2012), 1027-1040
##[24]
L. J. Lin, Q. H. Ansari, J. Y. Wu, Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems, J. Optim. Theory Appl., 117 (2003), 121-137
##[25]
T. Tanino, Stability and sensitivity analysis in convex vector optimization, SIAM J. Control Optim., 26 (1988), 521-536
##[26]
Q.-L. Wang, S.-J. Li, Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem, J. Ind. Manag. Optim., 10 (2014), 1225-1234
##[27]
Q.-L. Wang, Z. Lin, X. B. Li, Semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem, Positivity, 18 (2014), 733-748
##[28]
Y. D. Xu, S. J. Li, On the lower semicontinuity of the solution mappings to a parametric generalized strong vector equilibrium problem, Positivity, 17 (2013), 341-353
]
Inclusion relationships for certain subclasses of analytic functions involving linear operator
Inclusion relationships for certain subclasses of analytic functions involving linear operator
en
en
Based on a linear operator, some new subclasses of analytic and univalent functions are introduced. The object of the
present paper is to derive inclusion relationships for these classes. Some applications of the inclusion results are also obtained.
2689
2699
Yan
Chen
School of Information and Mathematics
Yangtze University
P. R. China
191399718@qq.com
Xiaofei
Li
School of Information and Mathematics
Department of Mathematics
Yangtze University
University of Macau
P. R. China
P. R. China
lxfei0828@163.com
Chuan
Qin
Yangtze University College of Engineering and Technology
P. R. China
qinchuan0920@163.com
Analytic functions
univalent functions
subordination
Hadamard product
linear operator.
Article.35.pdf
[
[1]
B. C. Carlson, D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 159 (1984), 737-745
##[2]
N. E. Cho, O. S. Kwon, H. M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292 (2004), 470-483
##[3]
J. H. Choi, M. Saigo, H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276 (2002), 432-445
##[4]
R. M. Goel, N. S. Sohi, A new criterion for p-valent functions, Proc. Amer. Math. Soc., 78 (1980), 353-357
##[5]
W. C. Ma, D. Minda, A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis, Tianjin, (1992), Conf. Proc. Lecture Notes Anal., Int. Press, Cambridge, MA, 1 (1994), 157-169
##[6]
S. S. Miller, P. T. Mocanu, Differential subordinations, Theory and applications, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (2000)
##[7]
M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A Math. Sci., 69 (1993), 234-237
##[8]
J. Patel, A. K. Mishra, On certain subclasses of multivalent functions associated with an extended fractional differintegral operator, J. Math. Anal. Appl., 332 (2007), 109-122
##[9]
H. Saitoh, A linear operator and its applications of first order differential subordinations, Math. Japon., 44 (1996), 31-38
##[10]
H. M. Srivastava, S. M. Khairnar, M. More, Inclusion properties of a subclass of analytic functions defined by an integral operator involving the Gauss hypergeometric function, Appl. Math. Comput., 218 (2011), 3810-3821
]
Strong-weak convergence of two algorithms for total asymptotically nonexpansive mappings
Strong-weak convergence of two algorithms for total asymptotically nonexpansive mappings
en
en
The purpose of this article is to investigate fixed point problems of total asymptotically nonexpansive mappings via two
different iterative algorithms. We obtain strong and convergence theorems in the framework of Hilbert spaces. The main results
improve and extend the recent corresponding results.
2700
2709
Yan
Hao
School of Mathematics, Physics and Information Science
Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Zhejiang Ocean University
China
China
zjhaoyan@yeah.net
Chaoping
Wang
School of Mathematics, Physics and Information Science
Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Zhejiang Ocean University
China
China
Jie
Zhou
School of Mathematics, Physics and Information Science
Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Zhejiang Ocean University
China
China
Hilbert space
convergence analysis
iterative algorithm
total asymptotically nonexpansive mappings
projection.
Article.36.pdf
[
[1]
R. P. Agarwal, X.-L. Qin, S. M. Kang, An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2011 (2011), 1-17
##[2]
Y. I. Alber, C. E. Chidume, H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2006 (2006), 1-20
##[3]
I. K. Argyros, S. George, S. M. Erappa, Expanding the applicability of the generalized Newton method for generalized equations, Commun. Optim. Theory, 2017 (2017), 1-12
##[4]
B. A. Bin Dehaish, A. Latif, H. O. Bakodah, X.-L. Qin, A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 1-14
##[5]
R. Bruck, T. Kuczumow, S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math., 65 (1993), 169-179
##[6]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2014), 103-120
##[7]
S. Y. Cho, B. A. Bin Dehaish, X.-L. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427-438
##[8]
S. Y. Cho, W.-L. Li, S. M. Kang, Convergence analysis of an iterative algorithm for monotone operators, J. Inequal. Appl., 2013 (2013), 1-14
##[9]
N.-N. Fang, Y.-P. Gong, Viscosity iterative methods for split variational inclusion problems and fixed point problems of a nonexpansive mapping , Commun. Optim. Theory, 2016 (2016), 1-15
##[10]
A. Genel, J. Lindenstrauss, An example concerning fixed points, Israel J. Math., 22 (1975), 81-86
##[11]
K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174
##[12]
Z.-Y. Huang, Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 37 (1999), 1-7
##[13]
S. H. Khan, H. Fukhar-ud-din, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal., 61 (2005), 1295-1301
##[14]
J. K. Kim, S. Y. Cho, X.-L. Qin, Some results on generalized equilibrium problems involving strictly pseudocontractive mappings, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 2041-2057
##[15]
M. Maiti, M. K. Ghosh, Approximating fixed points by Ishikawa iterates, Bull. Austral. Math. Soc., 40 (1989), 113-117
##[16]
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591-597
##[17]
H. Piri, R. Yavarimehr, Solving systems of monotone variational inequalities on fixed point sets of strictly pseudocontractive mappings, J. Nonlinear Funct. Anal., 2016 (2016), 1-18
##[18]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488-502
##[19]
X.-L. 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
##[20]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 1-9
##[21]
S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67 (1979), 274-276
##[22]
J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158 (1991), 407-413
##[23]
J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43 (1991), 153-159
##[24]
K.-K. Tan, H.-K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178 (1993), 301-308
##[25]
H. Zegeye, W. W. Kassu, M. G. Sangago, Common fixed points of a finite family of multi-valued rho-nonexpansive mappings in modular function spaces, Commun. Optim. Theory, 2016 (2016), 1-14
]
Positive solutions for a class of integral boundary value condition of fractional differential equations with a parameter
Positive solutions for a class of integral boundary value condition of fractional differential equations with a parameter
en
en
In this work, we study a class of integral boundary value condition of fractional differential equations with a parameter.
The existence and uniqueness of positive solutions to the boundary value problem is established. Further, we present some
properties of positive solutions to the boundary value problem dependent on the parameter. The method employed is a fixed
point theorem of concave operators in partial ordering Banach spaces. As applications, two examples are given to illustrate our
main results.
2710
2718
Chen
Yang
Basic Course Department
Business College of Shanxi University
P. R. China
yangchen0809@126.com
Fractional order derivative
positive solution
parameter
fixed point theorem of concave operator
integral boundary value condition.
Article.37.pdf
[
[1]
B. Ahmad, S. Sivasundaram, Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Anal. Hybrid Syst., 4 (2010), 134-141
##[2]
A. Cabada, Z. Hamdi, Nonlinear fractional differential equations with integral boundary value conditions, Appl. Math. Comput., 228 (2014), 251-257
##[3]
A. Cabada, G.-T. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions, J. Math. Anal. Appl., 389 (2012), 403-411
##[4]
Y. Du, Fixed points of a class of noncompact operator and its application, (in Chinese), Acta Mathematica Sinica, 32 (1989), 618-627
##[5]
M.-Q. Feng, X.-M. Zhang, W.-G. Ge, New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions, Bound. Value Probl., 2011 (2011), 1-20
##[6]
D. J. Guo, V. Lakshmikantham, Nonlinear problems in abstract cones, Notes and Reports in Mathematics in Science and Engineering, Academic Press, Inc., Boston, MA (1988)
##[7]
M. Jiang, S.-M. Zhong, Successively iterative method for fractional differential equations with integral boundary conditions, Appl. Math. Lett., 38 (2014), 94-99
##[8]
M. A. Krasnosel'skiĭ, Positive solutions of operator equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron, Noordhoff Ltd., Groningen (1964)
##[9]
S.-J. Li, X.-U. Zhang, Y.-H. Wu, L. Caccetta, Extremal solutions for p-Laplacian differential systems via iterative computation, Appl. Math. Lett., 26 (2013), 1151-1158
##[10]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[11]
Y.-P. Sun, M. Zhao, Positive solutions for a class of fractional differential equations with integral boundary conditions, Appl. Math. Lett., 34 (2014), 17-21
##[12]
C. Yang, C.-B. Zhai, Uniqueness of positive solutions for a fractional differential equation via a fixed point theorem of a sum operator, Electron. J. Differential Equations, 2012 (2012), 1-8
##[13]
C.-J. Yuan, Multiple positive solutions for (n - 1, 1)-type semipositone conjugate boundary value problems of nonlinear fractional differential equations, Electron. J. Qual. Theory Differ. Equ., 2010 (2010), 1-12
##[14]
C.-B. Zhai, M.-R. Hao, Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems, Nonlinear Anal., 75 (2012), 2542-2551
##[15]
C.-B. Zhai, L. Xu, Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 2820-2827
##[16]
C.-B. Zhai, W.-P. Yan, C. Yang, A sum operator method for the existence and uniqueness of positive solutions to Riemann- Liouville fractional differential equation boundary value problems, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 858-66
##[17]
X.-Q. Zhang, L. Wang, Q. Sun, Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter, Appl. Math. Comput., 226 (2014), 708-718
##[18]
X.-K. Zhao, C.-W. Chai, W.-G. Ge, Existence and nonexistence results for a class of fractional boundary value problems, J. Appl. Math. Comput., 41 (2013), 17-31
]
An affirmative answer to Panyanak and Suantai's open question on the viscosity approximation methods for a nonexpansive multi-valued mapping in CAT(0) spaces
An affirmative answer to Panyanak and Suantai's open question on the viscosity approximation methods for a nonexpansive multi-valued mapping in CAT(0) spaces
en
en
An affirmative answer to the open question raised by Panyanak and Suantai [B. Panyanak, S. Suantai, Fixed Point Theory
Appl., 2015 (2015), 14 pages] is given. Our results also generalize the results of Panyanak and Suantai [B. Panyanak, S. Suantai,
Fixed Point Theory Appl., 2015 (2015), 14 pages], Wangkeeree and Preechasilp [R. Wangkeeree, P. Preechasilp, J. Inequal. Appl.,
2013 (2013), 15 pages], Dhompongsa et al. [S. Dhompongsa, A. Kaewkhao, B. Panyanak, Nonlinear Anal., 75 (2012), 459–468],
and many others. Some related results in R-trees are also proved.
2719
2726
Shih-Sen
Chang
Center for General Education
China Medical University
Taiwan
changss2013@163.com
Lin
Wang
College of Statistics and Mathematics
Yunnan University of Finance and Economics
China
wanglin64@outlook.com
Jen-Chih
Yao
Center for General Education
China Medical University
Taiwan
yaojc@mail.cmu.edu.tw
Li
Yang
Department of Mathematics
South West University of Science and Technology
China
yangli@swust.edu.cn
Viscosity approximation method
fixed point
strong convergence
multivalued nonexpansive mapping
CAT(0) space.
Article.38.pdf
[
[1]
A. G. Aksoy, M. A. Khamsi, A selection theorem in metric trees, Proc. Amer. Math. Soc., 134 (2006), 2957-2966
##[2]
I. D. Berg, I. G. Nikolaev, Quasilinearization and curvature of Aleksandrov spaces, Geom. Dedicata, 133 (2008), 195-218
##[3]
M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (1999)
##[4]
K. S. Brown, Buildings, Springer-Verlag, New York (1989)
##[5]
S. Dhompongsa, A. Kaewkhao, B. Panyanak , Browder’s convergence theorem for multivalued mappings without endpoint condition, Topology Appl., 159 (2012), 2757-2763
##[6]
S. Dhompongsa, A. Kaewkhao, B. Panyanak, On Kirk’s strong convergence theorem for multivalued nonexpansive mappings on CAT(0) spaces, Nonlinear Anal., 75 (2012), 459-468
##[7]
S. Dhompongsa, W. A. Kirk, B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8 (2007), 35-45
##[8]
S. Dhompongsa, B. Panyanak, On \(\Delta\)-convergence theorems in CAT(0) spaces , Comput. Math. Appl., 56 (2008), 2572-2579
##[9]
K. Goebel, S. Reich, Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (1984)
##[10]
B. Gunduz, S. H. Khan, S. Akbulut, Common fixed points of two finite families of nonexpansive mappings in Kohlenbach hyperbolic spaces, J. Nonlinear Funct. Anal., 2015 (2015), 1-13
##[11]
W. A. Kirk, Fixed point theorems in CAT(0) spaces and R-trees, Fixed Point Theory Appl., 2004 (2004), 309-316
##[12]
J. T. Markin, Fixed points for generalized nonexpansive mappings in R-trees, Comput. Math. Appl., 62 (2011), 4614-4618
##[13]
A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
##[14]
S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-487
##[15]
B. Panyanak, S. Suantai, Viscosity approximation methods for multivalued nonexpansive mappings in geodesic spaces, Fixed Point Theory Appl., 2015 (2015), 1-14
##[16]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488-502
##[17]
L. Y. Shi, R. D. Chen, Strong convergence of viscosity approximation methods for nonexpansive mappings in CAT(0) spaces, J. Appl. Math., 2012 (2012), 1-11
##[18]
N. Shioji, W. Takahashi, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc., 125 (1997), 3641-3645
##[19]
R.Wangkeeree, P. Preechasilp, Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces, J. Inequal. Appl., 2013 (2013), 1-15
##[20]
R. Wangkeeree, P. Preechasilp, Viscosity approximation methods for nonexpansive semigroups in CAT(0) spaces, Fixed Point Theory Appl., 2013 (2013), 1-16
##[21]
H.-K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl., 116 (2003), 659-678
]
Oscillation of nonlinear second-order neutral delay differential equations
Oscillation of nonlinear second-order neutral delay differential equations
en
en
By using a couple of Riccati substitutions, we establish several new oscillation criteria for a class of second-order nonlinear
neutral delay differential equations. These results complement and improve the related contributions reported in the literature.
2727
2734
Jiashan
Yang
School of Information and Electronic Engineering
Wuzhou University
P. R. China
Jingjing
Wang
School of Information Science & Technology
Qingdao University of Science & Technology
P. R. China
Xuewen
Qin
School of Information and Electronic Engineering
Wuzhou University
P. R. China
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Informatics
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
Oscillation
neutral differential equation
nonlinear equation
delayed argument
Riccati substitution.
Article.39.pdf
[
[1]
R. P. Agarwal, M. Bohner, W.-T. Li, Nonoscillation and oscillation: theory for functional differential equations, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (2004)
##[2]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput., 225 (2013), 787-794
##[3]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math., 30 (2014), 1-6
##[4]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, Oscillation of second-order Emden–Fowler neutral delay differential equations, Ann. Mat. Pura Appl., 193 (2014), 1861-1875
##[5]
R. P. Agarwal, C.-H. Zhang, T.-X. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput., 274 (2016), 178-181
##[6]
B. Baculíková, J. Džurina, Oscillation theorems for second order neutral differential equations, Comput. Math. Appl. , 61 (2011), 94-99
##[7]
B. Baculíková, J. Džurina, Oscillation theorems for second-order nonlinear neutral differential equations, Comput. Math. Appl., 62 (2011), 4472-4478
##[8]
B. Baculíková, T.-X. Li, J. Džurina, Oscillation theorems for second-order superlinear neutral differential equations, Math. Slovaca, 63 (2013), 123-134
##[9]
Z.-L. Han, T.-X. Li, S.-R. Sun, Y.-B. Sun, Remarks on the paper [Appl. Math. Comput. 207 (2009) 388–396], Appl. Math. Comput., 215 (2010), 3998-4007
##[10]
M. Hasanbulli, Yu. V. Rogovchenko, Oscillation criteria for second order nonlinear neutral differential equations, Appl. Math. Comput., 215 (2010), 4392-4399
##[11]
T.-X. Li, R. P. Agarwal, M. Bohner, Some oscillation results for second-order neutral dynamic equations, Hacet. J. Math. Stat., 41 (2012), 715-721
##[12]
T.-X. Li, Yu. V. Rogovchenko, Oscillatory behavior of second-order nonlinear neutral differential equations, Abstr. Appl. Anal., 2014 (2014), 1-8
##[13]
T.-X. Li, Yu. V. Rogovchenko, Oscillation theorems for second-order nonlinear neutral delay differential equations, Abstr. Appl. Anal., 2014 (2014), 1-5
##[14]
T.-X. Li, Yu. V. Rogovchenko, Oscillation of second-order neutral differential equations, Math. Nachr., 288 (2015), 1150-1162
##[15]
T.-X. Li, Yu. V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett., 61 (2016), 35-41
##[16]
T.-X. Li, Yu. V. Rogovchenko, C.-H. Zhang, Oscillation of second-order neutral differential equations, Funkcial. Ekvac., 56 (2013), 111-120
##[17]
T.-X. Li, Yu. V. Rogovchenko, C.-H. Zhang, Oscillation results for second-order nonlinear neutral differential equations, Adv. Difference Equ., 2013 (2013), 1-13
##[18]
F.-W. Meng, R. Xu, Kamenev-type oscillation criteria for even order neutral differential equations with deviating arguments, Appl. Math. Comput., 190 (2007), 1402-1408
##[19]
F.-W. Meng, R. Xu, Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments, Appl. Math. Comput., 190 (2007), 458-464
##[20]
X.-L. Wang, F.-W. Meng, Oscillation criteria of second-order quasi-linear neutral delay differential equations, Math. Comput. Modelling, 46 (2007), 415-421
##[21]
G.-J. Xing, T.-X. Li, C.-H. Zhang, Oscillation of higher-order quasi-linear neutral differential equations, Adv. Difference Equ., 2011 (2011), 1-10
##[22]
R. Xu, F.-W. Meng, New Kamenev-type oscillation criteria for second order neutral nonlinear differential equations, Appl. Math. Comput., 188 (2007), 1364-1370
##[23]
R. Xu, F.-W. Meng, Oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput., 192 (2007), 216-222
##[24]
J.-S. Yang, X.-W. Qin, Oscillation criteria for certain second-order Emden–Fowler delay functional dynamic equations with damping on time scales, Adv. Difference Equ., 2015 (2015), 1-16
##[25]
L.-H. Ye, Z.-T. Xu, Oscillation criteria for second order quasilinear neutral delay differential equations, Appl. Math. Comput, 207 (2009), 388-396
##[26]
C.-H. Zhang, R. P. Agarwal, M. Bohner, T.-X. Li, New oscillation results for second-order neutral delay dynamic equations, Adv. Difference Equ., 2012 (2012), 1-14
##[27]
J.-H. Zhao, F.-W. Meng, Oscillation criteria for second-order neutral equations with distributed deviating argument, Appl. Math. Comput., 206 (2008), 485-493
##[28]
J.-C. Zhong, Z.-G. Ouyang, S.-L. Zou, An oscillation theorem for a class of second-order forced neutral delay differential equations with mixed nonlinearities, Appl. Math. Lett., 24 (2011), 1449-1454
]
Study on convergence and stability of a conservative difference scheme for the generalized Rosenau-KdV equation
Study on convergence and stability of a conservative difference scheme for the generalized Rosenau-KdV equation
en
en
In this paper, a conservative nonlinear implicit finite difference scheme for the generalized Rosenau-KdV equation is studied.
Convergence and stability of the proposed scheme are proved by a discrete energy method. The proof with a priori error estimate
shows that the convergence rates of numerical solutions are both the second order on time and in space. Meanwhile, numerical
experiments are carried out to verify the theoretical analysis and show that the scheme is efficient and reliable.
2735
2742
Jun
Zhou
School of Mathematics and Statistics
Yangtze Normal University
China
flzjzklm@126.com
Maobo
Zheng
Chengdu Technological University
China
377178554@qq.com
Xiaomin
Dai
Mathematics Teaching and Research Group
Fifth Middle school of Fuling
China
15823657767@163.com
Rosenau-KdV equation
finite difference scheme
conservation
convergence
stability.
Article.40.pdf
[
[1]
K. Cheng, W.-Q. Feng, S. Gottlieb, C. Wang, A Fourier pseudospectral method for the ”good” Boussinesq equation with second-order temporal accuracy, Numer. Methods Partial Differential Equations, 31 (2015), 202-224
##[2]
S. K. Chung, Finite difference approximate solutions for the Rosenau equation, Appl. Anal., 69 (1998), 149-156
##[3]
G. Ebadi, A. Mojaver, H. Triki, A. Yildirim, A. Biswas, Topological solitons and other solutions of the Rosenau-KdV equation with power law nonlinearity, Romanian J. Phys., 58 (2013), 3-14
##[4]
A. Esfahani, Solitary wave solutions for generalized Rosenau-KdV equation, Commun. Theor. Phys. (Beijing), 55 (2011), 396-398
##[5]
J.-S. Hu, Y.-C. Xu, B. Hu, Conservative linear difference scheme for Rosenau-KdV equation, Adv. Math. Phys., 2013 (2013), 1-7
##[6]
J.-S. Hu, K.-L. Zheng, Two conservative difference schemes for the generalized Rosenau equation, Bound. Value Probl., 2010 (2010), 1-18
##[7]
Y. Luo, Y.-C. Xu, M.-F. Feng, Conservative difference scheme for generalized Rosenau-KdV equation, Adv. Math. Phys., 2014 (2014), 1-7
##[8]
K. Omrani, F. Abidi, T. Achouri, N. Khiari, A new conservative finite difference scheme for the Rosenau equation, Appl. Math. Comput., 201 (2008), 35-43
##[9]
P. Razborova, H. Triki, A. Biswas, Perturbation of dispersive shallow water waves, Ocean Eng., 63 (2013), 1-7
##[10]
A. Saha, Topological 1-soliton solutions for the generalized Rosenau-KdV equation, Fund. J. Math. Phys., 2 (2012), 19-25
##[11]
X.-J. Yang, A new integral transform method for solving steady heat-transfer problem, Therm. Sci., 20 (2016), 1-639
##[12]
X.-J. Yang, A new integral transform operator for solving the heat-diffusion problem, Appl. Math. Lett., 64 (2017), 193-197
##[13]
X.-J. Yang, F. Gao, A new technology for solving diffusion and heat equations, Therm. Sci., 21 (2017), 133-140
##[14]
X.-J. Yang, J. A. Tenreiro Machado, D. Baleanu, C. Cattani, On exact traveling-wave solutions for local fractional Korteweg-de Vries equation, Chaos, 26 (2016), 1-5
##[15]
K.-L. Zheng, J.-S. Hu, High-order conservative Crank-Nicolson scheme for regularized long wave equation, Adv. Difference Equ., 2016 (2013), 1-12
##[16]
M.-B. Zheng, J. Zhou, An average linear difference scheme for the generalized Rosenau-KdV equation, J. Appl. Math., 2014 (2014), 1-9
##[17]
Y. L. Zhou, Applications of discrete functional analysis to the finite difference method, International Academic Publishers, Beijing (1991)
##[18]
J. Zhou, M.-B. Zheng, R.-X. Jiang, The conservative difference scheme for the Generalized Rosenau-KDV equation, Therm. Sci., 20 (2016), 1-903
##[19]
J.-M. Zuo, Y.-M. Zhang, T.-D. Zhang, F. Chang, A new conservative difference scheme for the general Rosenau-RLW equation, Bound. Value Probl., 2010 (2010), 1-13
]
More general viscosity implicit midpoint rule for nonexpansive mapping with applications
More general viscosity implicit midpoint rule for nonexpansive mapping with applications
en
en
The more general viscosity implicit midpoint rule of fixed point of nonexpansive mapping in Hilbert space is established.
The strong convergence of this rule is proved under certain assumptions imposed on the sequence of parameters, which, in
addition, is the unique solution of the variational inequality problem. Applications to variational inequalities, hierarchical
minimization problems, Fredholm integral equations, and nonlinear evolution equations are included. The results presented in
this work may be treated as an improvement, extension and refinement of some corresponding ones in the literature.
2743
2756
Hui-Ying
Hu
Department of Mathematics
Shanghai Normal University
China
huiying1117@hotmail.com
More general viscosity implicit midpoint rule
nonexpansive mapping
fixed point problem
iterative scheme
variational inequality.
Article.41.pdf
[
[1]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H.-K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory. Appl., 2014 (2014), 1-9
##[2]
H. Attouch, Viscosity solutions of minimization problems, SIAM J. Optim., 6 (1996), 769-806
##[3]
W. Auzinger, R. Frank, Asymptotic error expansions for stiff equations: an analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case, Numer. Math., 56 (1989), 469-499
##[4]
G. Bader, P. Deuflhard, A semi-implicit mid-point rule for stiff systems of ordinary differential equations, Numer. Math., 41 (1983), 373-398
##[5]
F. E. Browder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. U.S.A., 53 (1965), 1100-1103
##[6]
F. E. Browder, Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces, Arch. Rational Mech. Anal., 24 (1967), 82-90
##[7]
A. Cabot, Proximal point algorithm controlled by a slowly vanishing term: applications to hierarchical minimization, SIAM J. Optim., 15 (2005), 555-572
##[8]
P. Deuflhard, Recent progress in extrapolation methods for ordinary differential equations, SIAM Rev., 27 (1985), 505-535
##[9]
B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 73 (1967), 957-961
##[10]
P.-L. Lions, Approximation de points fixes de contractions, (French) C. R. Acad. Sci. Paris Sér. A-B, 284 (1977), 1-1357
##[11]
G. Marino, H.-K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 318 (2006), 43-52
##[12]
A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
##[13]
S. H. Rizvi, General viscosity implicit midpoint rule for nonexpansive mapping, ArVix, 2016 (2016), 1-14
##[14]
C. Schneider, Analysis of the linearly implicit mid-point rule for differential-algebraic equations, Electron. Trans. Numer. Anal., 1 (1993), 1-10
##[15]
S. Somalia, Implicit midpoint rule to the nonlinear degenerate boundary value problems, Int. J. Comput. Math., 79 (2002), 327-332
##[16]
M. van Veldhuizen, Asymptotic expansions of the global error for the implicit midpoint rule (stiff case) , Computing, 33 (1984), 185-192
##[17]
H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[18]
H.-K. Xu, Averaged mappings and the gradient-projection algorithm, J. Optim. Theory Appl., 150 (2011), 360-378
##[19]
H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-12
##[20]
I. Yamada, The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications, Haifa, (2000), Stud. Comput. Math., North-Holland, Amsterdam, 8 (2001), 473-504
]
Boundedness of higher order Riesz transforms associated with Schrödinger type operator on generalized Morrey spaces
Boundedness of higher order Riesz transforms associated with Schrödinger type operator on generalized Morrey spaces
en
en
Let \(L_2 = (-\Delta)^2 + V^2\) be a Schrödinger type operator, where \(V \neq 0\) is a non-negative potential and belongs to the reverse
Hölder class \(RH_q\) for \(q \geq n/2, n\geq 5\). The higher Riesz transform associated with \(L_2\) is denoted by \(R = \nabla^2L_2^{\frac{-1}{2}}\)
and its dual is
denoted by \(R^* =L_2^{\frac{-1}{2}} \nabla^2\). In this paper, we investigate the boundedness of higher Riesz transforms and their commutators on
the generalized Morrey spaces related to some non-negative potential.
2757
2766
Bijun
Ren
Department of Information Engineering
Henan Institute of Finance and Banking
P. R. China
renbijun1959@163.com
Hui
Wang
Teachers College
Nanyang Institute of Technology
P. R. China
wanghui1639@126.com
Schrödinger operator
Riesz transform
commutator
BMO
generalized Morrey space.
Article.42.pdf
[
[1]
B. Bongioanni, E. Harboure, O. Salinas, Commutators of Riesz transforms related to Schrödinger operators, J. Fourier Anal. Appl., 17 (2011), 115-134
##[2]
D. X. Chen, F. T. Jin, The boundedness of Marcinkiewicz integrals associated with Schrödinger operator on Morrey spaces, J. Funct. Spaces, 2014 (2014), 1-11
##[3]
J. Dziubański, J. Zienkiewicz, \(H_p\) spaces associated with Schrödinger operators with potentials from reverse Hölder classes, Colloq. Math., 98 (2003), 5-38
##[4]
Y. Liu, J. F. Dong, Some estimates of higher order Riesz transform related to Schrödinger type operators, Potential Anal., 32 (2010), 41-55
##[5]
Y. Liu, L. J. Wang, Boundedness for Riesz transform associated with Schrödinger operators and its commutator on weighted Morrey spaces related to certain nonnegative potentials, J. Inequal. Appl., 2014 (2014), 1-16
##[6]
Y. Liu, J. Zhang, J.-L. Sheng, L.-J. Wang, Some estimates for commutators of Riesz transform associated with Schrödinger operators, Czechoslovak Math. J., 66 (2016), 169-191
##[7]
T. Mizuhara, Boundedness of some classical operators on generalized Morrey spaces, Harmonic analysis, ICM-90 Satell. Conf. Proc., Springer, Japan, (1991), 183-189
##[8]
C. B. Jr. Morrey, On the solutions of quasi-linear elliptic partial differential equations , Trans. Amer. Math. Soc., 43 (1938), 126-166
##[9]
G. Pan, L. Tang, Boundedness for some Schrödinger type operators on weighted Morrey spaces, J. Funct. Spaces, 2014 (2014), 1-10
##[10]
Z. Shen, \(L_p\) estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble), 45 (1995), 513-546
##[11]
L. Tang, J. F. Dong, Boundedness for some Schrödinger type operator on Morrey spaces related to certain nonnegative potentials, J. Math. Anal. Appl., 355 (2009), 101-109
##[12]
R. L. Wheeden, A. Zygmund, Measure and integral: An introduction to real analysis, Marcel Dekker Inc., New York (1977)
]
Identities for Korobov-type polynomials arising from functional equations and p-adic integrals
Identities for Korobov-type polynomials arising from functional equations and p-adic integrals
en
en
By using generating functions and their functional equations for the special numbers and polynomials, we derive various
identities and combinatorial sums including the Korobov-type polynomials, the Bernoulli numbers, the Stirling numbers, the
Daehee numbers and the Changhee numbers. Furthermore, by using the Volkenborn integral and the fermionic p-adic integral,
we also derive combinatorial sums associated with the Korobov-type polynomials, the Lah numbers, the Changhee numbers
and the Daehee numbers. Finally, we give a conclusion on our results.
2767
2777
Ahmet
Yardimci
Department of Biostatistics and Medical Informatics, Faculty of Medicine
University of Akdeniz
Turkey
yardimci@akdeniz.edu.tr
Yilmaz
Simsek
Department of Mathematics, Faculty of Science
University of Akdeniz
Turkey
ysimsek@akdeniz.edu.tr
Bernoulli numbers and polynomials
Euler numbers and polynomials
Daehee numbers and polynomials
Changhee numbers and polynomials
Lah numbers
Apostol-Daehee numbers
Korobov polynomials
Stirling numbers
generating functions
functional equation
p-adic integral.
Article.43.pdf
[
[1]
L. Comtet, Advanced combinatorics, The art of finite and infinite expansions, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht (1974)
##[2]
G. B. Djordjević, G. V. Milovanović, Special classes of polynomials, Faculty of Technology Leskovac, University of Nis, Nis, Serbia (2014)
##[3]
D. V. Dolgy, D. S. Kim, T. Kim , On the Korobov polynomials of the first kind, (Russian) Mat. Sb., 208 (2017), 65-79
##[4]
B. S. El-Desouky, A. Mustafa, New results and matrix representation for Daehee and Bernoulli numbers and polynomials, Appl. Math. Sci., 9 (2015), 3593-3610
##[5]
M. A. Guzev, A. V. Ustinov, Mechanical characteristics of molecular dynamics model and Korobov polynomials, (Russian) Dalnevost. Mat. Zh., 16 (2016), 39-43
##[6]
L. C. Jang, T. Kim, A new approach to q-Euler numbers and polynomials, J. Concr. Appl. Math., 6 (2008), 159-168
##[7]
T. Kim, An invariant p-adic integral associated with Daehee numbers, Integral Transforms Spec. Funct., 13 (2002), 65-69
##[8]
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys., 19 (2002), 288-299
##[9]
T. Kim, q-Euler numbers and polynomials associated with p-adic q-integral and basic q-zeta function, Trends Math., 9 (2006), 7-12
##[10]
T. Kim, On p-adic q-l-functions and sums of powers, J. Math. Anal. Appl., 329 (2007), 1472-1481
##[11]
T. Kim , On the analogs of Euler numbers and polynomials associated with p-adic q-integral on \(\mathbb{Z}_p\) at \(q = -1\), J. Math. Anal. Appl., 331 (2007), 779-792
##[12]
T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl., 326 (2007), 1458-1465
##[13]
T. Kim, An invariant p-adic q-integral on \(\mathbb{Z}_p\), Appl. Math. Lett., 21 (2008), 105-108
##[14]
D. S. Kim, T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. (Ruse), 7 (2013), 5969-5976
##[15]
T. Kim, D. S. Kim, Korobov polynomials of the third kind and of the fourth kind, SpringerPlus, 4 (2015), 1-23
##[16]
D. S. Kim, T. Kim, Some identities of degenerate special polynomials, Open Math., 13 (2015), 380-389
##[17]
D. S. Kim, T. Kim, Some identities of Korobov-type polynomials associated with p-adic integrals on \(\mathbb{Z}_p\), Adv. Difference Equ., 2015 (2015), 1-13
##[18]
D. S. Kim, T. Kim, J. J. Seo, A note on Changhee polynomials and numbers, Adv. Stud. Theor. Phys., 7 (2013), 993-1003
##[19]
T. Kim, S.-H. Rim, Some q-Bernoulli numbers of higher order associated with the p-adic q-integrals, Indian J. Pure Appl. Math., 32 (2001), 1565-1570
##[20]
T. Komatsu, Convolution identities for Cauchy numbers, Acta Math. Hungar., 144 (2014), 76-91
##[21]
N. M. Korobov, Special polynomials and their applications, Diophantine approximations, Math. Notes., 2 (1996), 77-89
##[22]
D. V. Kruchinin, Explicit formulas for Korobov polynomials, Proc. Jangjeon Math. Soc., 20 (2017), 43-50
##[23]
J. Riordan, An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London (1958)
##[24]
S. Roman, The umbral calculus, Pure and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York (1984)
##[25]
W. H. Schikhof, Ultrametric calculus, An introduction to p-adic analysis, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1984)
##[26]
Y. Simsek, Apostol type Daehee numbers and polynomials, Adv. Stud. Contemp. Math., 26 (2016), 555-566
##[27]
Y. Simsek, Computation methods for combinatorial sums and Eulertype numbers related to new families of numbers, Math. Methods Appl. Sci., 40 (2017), 2347-2361
##[28]
Y. Simsek, Formulas for p-adic q-integrals including falling-rising factorials, combinatorial sums and special numbers, ArXiv, 2017 (2017), 1-47
##[29]
Y. Simsek, H. M. Srivastava, Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications, Cogent Math., 3 (2016), 1-17
##[30]
Y. Simsek, A. Yardimci, Applications on the Apostol-Daehee numbers and polynomials associated with special numbers, polynomials, and p-adic integrals, Adv. Difference Equ., 308 (2016), 1-14
##[31]
H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci., 5 (2011), 390-444
##[32]
H. M. Srivastava, J.-S. Choi, Zeta and q-Zeta functions and associated series and integrals, Elsevier, Inc., Amsterdam (2012)
##[33]
H. M. Srivastava, T. Kim, Y. Simsek, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russ. J. Math. Phys., 12 (2005), 241-268
]
The exact controllability of Euler-Bernoulli beam systems with small delays in the boundary feedback controls
The exact controllability of Euler-Bernoulli beam systems with small delays in the boundary feedback controls
en
en
This work is concerned with the exact controllability of an Euler-Bernoulli beam system with small delays in the boundary
feedback controls
\[w_{tt}(x,t)+w_{xxxx}(x,t)=0,\quad x\in (0,1)\quad t>0, \] \[w(0,t)=w_x(0,t)=0,\quad t\geq 0,\] \[w_{xx}(1,1-\varepsilon)=-k_2^2 w_{tx}(1,t)-c_2w_t(1,t-\varepsilon),\quad \varepsilon>0,\quad k_1^2+k_2^2\neq 0,\] \[w_{xxx}(1,t)=k_1^2w_t(1,t-\varepsilon)-c_1w_{tx}(1,t-\varepsilon),\quad k_i,c_i\in R,\quad (i=1,2),\]
with boundary conditions
\[w(x,t)=\varphi(x,t), \quad w_t(x,t)=\psi(x,t), \quad -\varepsilon\leq t\leq 0.\]
Our analysis relies on the exact controllability on Hilbert space M and state space H. Our results based on formulating the
original system as a state linear system. We formulate the system as the state feedback control systems
\(\Sigma(A, B,C)\), and we get
the generalized eigenvectors of the operator A. Then we prove that they can form a Riesz basis for the state space H. In the end,
the system is proved to be exactly controllable on H.
2778
2787
Zhang
Zhuo
Basic Course Department
Business College of Shanxi University
P. R. China
zzswxy@126.com
Euler-Bernoulli beam
delay
boundary feedback control
exact controllability.
Article.44.pdf
[
[1]
Z.-Q. Ge, G.-T. Zhu, D.-X. Feng, Exact controllability for singular distributed parameter system in Hilbert space, Sci. China Ser. F, 52 (2009), 2045-2052
##[2]
G. C. Gorain, S. K. Bose, Exact controllability and boundary stabilization of flexural vibrations of an internally damped flexible space structure, Appl. Math. Comput., 126 (2002), 341-360
##[3]
L. Hu, F.-Q. Ji, K.Wang, Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations, Chin. Ann. Math. Ser. B, 34 (2013), 479-490
##[4]
K. Huang, Y.-J. Yin, F. Yang, Q.-S. Fan, A modified couple stress nonlinear theory for Bernoulli-Euler microbeam, 13th International Conference on Fracture (ICF13), Abstract Book, Beijing (2013)
##[5]
Y. Lü, Exact controllability for a class of nonlinear evolution control systems, Commun. Math. Res., 8 (2015), 285-288
##[6]
G.-C. Pang, K.-J. Zhang, Stability of time-delay system with time-varying uncertainties via homogeneous polynomial Lyapunov-Krasovskii functions, Inter. J. Autom. Comput., 12 (2015), 657-663
##[7]
R. Rebarber, Conditions for the equivalence of internal and external stability for distributed parameter systems, Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, UK, 3 (1991), 3008-3013
##[8]
M. Y. Robert, An introduction to nonharmonic Fourier series, Revised first edition, Academic Press, Inc., San Diego, CA (2001)
##[9]
Y.-T. Wang, G. Wang, S.-J. Li, On Riesz basis of Euler-Bernoulli beam system by boundary feedback controls, Acta Math. Sin. Chin. Ser., 2 (2000), 111-122
##[10]
L. Xu, S.-P. Shen, Size-dependent behavior in nano-dielectric Bernoulli-Euler beam, Abstract Book of 23rd International Congress of Theoretical and Applied Mechanics, (2012)
##[11]
R.-M. Yang, Y.-Z. Wang, Stability for a class of nonlinear time-delay systems via Hamiltonian functional method, Sci. China Inf. Sci., 55 (2012), 1218-1228
##[12]
F.-Y. Yang, P.-F. Yao, Exact controllability of the Euler-Bernoulli plate with variable coefficients and mixed boundary conditions, 34th Chinese Control Conference (CCC), Hangzhou, China, (2015), 1395-1400
##[13]
Y. Zhu, Q.-N. Gao, Y. Xiao, Sufficient conditions for stability of linear time-delay systems with dependent delays, J. Syst. Eng. Electron., 24 (2013), 845-851
]
Quantitative self adjoint operator direct approximations
Quantitative self adjoint operator direct approximations
en
en
Here we give a series of self adjoint operator positive linear operators general results. Then we present specific similar
results related to neural networks. This is a quantitative treatment to determine the degree of self adjoint operator uniform
approximation with rates, of sequences of self adjoint positive linear operators in general, and in particular of self adjoint
specific neural network operators. The approach is direct relying on Gelfand’s isometry.
2788
2797
George A.
Anastassiou
Department of Mathematical Sciences
University of Memphis
U.S.A
ganastss@memphis.edu
Self adjoint operator
Hilbert space
positive linear operator
Bernstein polynomials
neural network operators.
Article.45.pdf
[
[1]
G. A. Anastassiou, Quantitative approximations, Chapman & Hall/CRC, Boca Raton, FL (2001)
##[2]
G. A. Anastassiou, Intelligent systems: approximation by artificial neural networks, Intelligent Systems Reference Library, Springer-Verlag, Berlin (2011)
##[3]
G. A. Anastassiou, Intelligent systems II: complete approximation by neural network operators, Studies in Computational Intelligence, Springer, Cham (2016)
##[4]
G. A. Anastassiou, Self adjoint operator Korovkin type and polynomial direct approximations with rates, RGMIA Res. Rep. Coll., 19 (2016), 1-16
##[5]
S. S. Dragomir, Ostrowski’s type inequalities for continuous functions of self adjoint operators on Hilbert spaces: a survey of recent results, Ann. Funct. Anal., 2 (2011), 139-205
##[6]
S. S. Dragomir, Operator inequalities of Ostrowski and trapezoidal type, SpringerBriefs in Mathematics, Springer, New York (2012)
##[7]
G. Helmberg, Introduction to spectral theory in Hilbert space, North-Holland Series in Applied Mathematics and Mechanics, North-Holland Publishing Co., Amsterdam-London; Wiley Interscience Division John Wiley & Sons, Inc., New York (1969)
##[8]
C. A. McCarthy, \(c_p\), Israel J. Math., 5 (1967), 249-271
##[9]
J. Pečarić, T. Furuta, J. Mićić Hot, Y.-K. Seo, Mond-Pečarić method in operator inequalities, Inequalities for bounded self adjoint operators on a Hilbert space, Monographs in Inequalities, ELEMENT, Zagreb (2005)
]
Fourier series of sums of products of Bernoulli functions and their applications
Fourier series of sums of products of Bernoulli functions and their applications
en
en
We consider three types of sums of products of Bernoulli functions and derive their Fourier series expansions. In addition,
we express each of them in terms of Bernoulli functions.
2798
2815
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Lee-Chae
Jang
Graduate School of Education
Konkuk University
Republic of Korea
lcjang@konkuk.ac.kr
Gwan-Woo
Jang
Department of Mathematics
Kwangwoon University
Republic of Korea
jgw5687@naver.com
Fourier series
Bernoulli polynomials
Bernoulli functions.
Article.46.pdf
[
[1]
A. Bayad, T. Kim, Higher recurrences for Apostol-Bernoulli-Euler numbers, Russ. J. Math. Phys., 19 (2012), 1-10
##[2]
D. Ding, J.-Z. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 20 (2010), 7-21
##[3]
G. V. Dunne, C. Schubert, Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys., 7 (2013), 225-249
##[4]
C. Faber, R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math., 139 (2000), 173-199
##[5]
I. M. Gessel, On Miki’s identity for Bernoulli numbers, J. Number Theory, 110 (2005), 75-82
##[6]
L. C. Jang, T. Kim, D. J. Kang, A note on the Fourier transform of fermionic p-adic integral on \(\mathbb{Z}_p\), J. Comput. Anal. Appl., 11 (2009), 571-575
##[7]
T. Kim, q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients, Russ. J. Math. Phys., 15 (2008), 51-57
##[8]
T. Kim, A note on the Fourier transform of p-adic q-integrals on \(\mathbb{Z}_p\), J. Comput. Anal. Appl., 11 (2009), 81-85
##[9]
T. Kim, Some identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials , Adv. Stud. Contemp. Math. (Kyungshang), 20 (2010), 23-28
##[10]
D. S. Kim, T. Kim, Bernoulli basis and the product of several Bernoulli polynomials, Int. J. Math. Math. Sci., 2012 (2012), 1-12
##[11]
D. S. Kim, T. Kim, A note on higher-order Bernoulli polynomials, J. Inequal. Appl., 2013 (2013), 1-9
##[12]
D. S. Kim, T. Kim, Some identities of higher order Euler polynomials arising from Euler basis, Integral Transforms Spec. Funct., 24 (2013), 734-738
##[13]
D. S. Kim, T. Kim, S.-H. Lee, D. V. Dolgy, S.-H. Rim, Some new identities on the Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc., 2011 (2011), 1-11
##[14]
H. Miki, A relation between Bernoulli numbers, J. Number Theory, 10 (1978), 297-302
##[15]
K. Shiratani, On some relations between Bernoulli numbers and class numbers of cyclotomic fields, Mem. Fac. Sci. Kyushu Univ. Ser. A, 18 (1964), 127-135
##[16]
K. Shiratani, S. Yokoyama, An application of p-adic convolutions, Mem. Fac. Sci. Kyushu Univ. Ser. A, 36 (1982), 73-83
##[17]
L. C. Washington, Introduction to cyclotomic fields, Second edition, Graduate Texts in Mathematics, Springer-Verlag, New York (1997)
##[18]
D. G. Zill, M. R. Cullen, Advanced engineering mathematics, Second edition, Jones and Bartlett Publishers, Massachusetts (2000)
]
Hybrid projection algorithms for finite total asymptotically strict quasi-\(\phi\)-pseudo-contractions
Hybrid projection algorithms for finite total asymptotically strict quasi-\(\phi\)-pseudo-contractions
en
en
The purpose of this article is to prove strong convergence theorems for finding a common fixed point of finite total asymptotically
strict quasi-\(\phi\)-pseudo-contractions by using a hybrid projection algorithm in Banach spaces. As applications, we apply
our main results to find a common solution of a system of generalized mixed equilibrium problems. Finally, some results of
numerical simulations are given for supporting our results.
2816
2827
Xiaomei
Zhang
Department of Foundation
Shandong Yingcai University
P. R. China
xiaomeizhang0717@hotmail.com
Qiuhong
Cao
Department of Otorhinolaryngology
Head and Neck Surgery
P. R. China
qiuhongcao@126.com
Zi-Ming
Wang
Department of Foundation
Shandong Yingcai University
P. R. China
wangziming@ymail.com
Total asymptotically strict quasi-\(\phi\)-pseudo-contraction
generalized mixed equilibrium problem
fixed point
Banach space
hybrid method.
Article.47.pdf
[
[1]
R. P. Agarwal, Y. J. Cho, X.-L. Qin, Generalized projection algorithms for nonlinear operators, Numer. Funct. Anal. Optim., 28 (2007), 1197-1215
##[2]
Y. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York, 178 (1996), 15-50
##[3]
D. Butnariu, S. Reich, A. J. Zaslavski, Asymptotic behavior of relatively nonexpansive operators in Banach spaces, J. Appl. Anal., 7 (2001), 151-174
##[4]
S. Y. Cho, B. A. Bin Dehaish, X.-L. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427-438
##[5]
Y. J. Cho, X-L. Qin, Systems of generalized nonlinear variational inequalities and its projection methods, Nonlinear Anal., 69 (2008), 4443-4451
##[6]
Y. J. Cho, X.-L. Qin, J. I. Kang, Convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems, Nonlinear Anal., 71 (2009), 4203-4214
##[7]
N.-N. Fang, Y.-P. Gong, Viscosity iterative methods for split variational inclusion problems and fixed point problems of a nonexpansive mapping, Commun. Optim. Theory, 2016 (2016), 1-15
##[8]
A. Genel, J. Lindenstrauss, An example concerning fixed points, Israel J. Math., 22 (1975), 81-86
##[9]
O. Güler, On the convergence of the proximal point algorithm for convex minimization, SIAM J. Control Optim., 29 (1991), 403-419
##[10]
Y. Haugazeau, Sur les inéquations variationnelles et la minimisation de fonctionnelles convexes, Thése, Université de Paris, Paris, France (1968)
##[11]
S. Kamimura, W. Takahashi, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim., 13 (2002), 938-945
##[12]
J. K. Kim, S. Y. Cho, X.-L. Qin, Some results on generalized equilibrium problems involving strictly pseudocontractive mappings, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 2041-2057
##[13]
S.-Y. Matsushita, W. Takahashi, Approximating fixed points of nonexpansive mappings in a Banach space by metric projections, Appl. Math. Comuput., 196 (2008), 422-425
##[14]
H. Piri, Strong convergence of the CQ method for fixed points of semigroups of nonexpansive mappings, J. Nonlinear Funct. Anal., 2015 (2015), 1-21
##[15]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488-502
##[16]
X.-L. Qin, S. Y. Cho, S. K. Kang, On hybrid projection methods for asymptotically quasi-\(\phi\)-nonexpansive mappings, Appl. Math. Comput., 215 (2010), 3874-3883
##[17]
X.-L. Qin, L. Wang, S. M. Kang, Some results on fixed points of asymptotically strict quasi-\(\varphi\)-pseudocontractions in the intermediate sense, Fixed Point Theory Appl., 2012 (2012), 1-18
##[18]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 1-9
##[19]
S. Reich, A weak convergence theorem for the alternating method with Bregman distances, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York, 178 (1996), 313-318
##[20]
O. Scherzer, Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems, J. Math. Anal. Appl., 194 (1995), 911-933
##[21]
Y.-F. Su, Z.-M.Wang, H.-K. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal., 71 (2009), 5616-5628
##[22]
Z.-M.Wang, Y.-F. Su, D.-X.Wang, Y.-C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relatively nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math., 235 (2011), 2364-2371
##[23]
Z.-M. Wang, J.-G. Yang, Hybrid projection algorithms for total asymptotically strict quasi-\(\phi\)-pseudo-contractions, J. Nonlinear Sci. Appl., 8 (2015), 1032-1047
##[24]
Z.-M. Wang, X.-M. Zhang, Shrinking projection methods for systems of mixed variational inequalities of Browder type, systems of mixed equilibrium problems and fixed point problems, J. Nonlinear Funct. Anal., 2014 (2014), 1-25
##[25]
C. Wu, G. Wang, Hybrid projection algorithms for asymptotically quasi-phi-nonexpansive mappings, Commun. Optim. Theory, 2013 (2013), 1-10
##[26]
S.-S Zhang, Generalized mixed equilibrium problem in Banach spaces, Appl. Math. Mech. (English Ed.), 30 (2009), 1105-1112
##[27]
H.-Y. Zhou, X.-H. Gao, An iterative method of fixed points for closed and quasi-strict pseudo-contractions in Banach spaces, J. Appl. Math. Comput., 33 (2010), 227-237
##[28]
H.-Y. Zhou, G.-L. 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
]
Some results on strong convergence for nonlinear maps in Banach spaces
Some results on strong convergence for nonlinear maps in Banach spaces
en
en
In this paper, an equilibrium problem which is also known as the Ky Fan inequality is investigated based on a fixed point
method. Strong convergence theorems for solutions of the equilibrium problem are established in the framework of reflexive
Banach spaces. Applications are also provided to support the main results.
2828
2836
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Adnan Salem
Alhomaidan
Department of Mathematics
King Abdulaziz University
Saudi Arabia
Xiaolong
Qin
Institute of Fundamental and Frontier Sciences
University of Electronic Science and Technology of China
China
qxlxajh@163.com
Equilibrium problem
fixed point
nonexpansive mapping
variational inequality
hybrid method.
Article.48.pdf
[
[1]
R. P. Agarwal, Y. J. Cho, X.-L. Qin, Generalized projection algorithms for nonlinear operators, Numer. Funct. Anal. Optim., 28 (2007), 1197-1215
##[2]
R. Ahmad, M. Akram, H. A. Rizvi, Generalized f-vector equilibrium problem, Commun. Optim. Theory, 2014 (2014), 1-11
##[3]
Y. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York, 178 (1996), 15-50
##[4]
B. A. Bin Dehaish, X.-L. 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
##[5]
E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145
##[6]
D. Butnariu, S. Reich, A. J. Zaslavski, Asymptotic behavior of relatively nonexpansive operators in Banach spaces, J. Appl. Anal., 7 (2001), 151-174
##[7]
S. Y. Cho, B. A. Bin Dehaish, X.-L. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427-438
##[8]
S. Y. Cho, X.-L. Qin, L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-15
##[9]
I. Cioranescu, Geometry of Banach spaces, duality mappings and nonlinear problems, Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht (1990)
##[10]
K. Fan, A minimax inequality and applications, Inequalities, III (Proc. Third Sympos., Univ. California, Los Angeles, Calif., 1969; dedicated to the memory of Theodore S. Motzkin), Academic Press, New York, (1972), 103-113
##[11]
N.-N. Fang, Some results on split variational inclusion and fixed point problems in Hilbert spaces, Commun. Optim. Theory, 2017 (2017), 1-13
##[12]
J. García Falset, W. Kaczor, T. Kuczumow, S. Reich, Weak convergence theorems for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal., 43 (2001), 377-401
##[13]
H. Hudzik, W. Kowalewski, G. Lewicki, Approximate compactness and full rotundity in Musielak-Orlicz spaces and Lorentz-Orlicz spaces, Z. Anal. Anwend., 25 (2006), 163-192
##[14]
X.-L. Qin, Y. J. Cho, S. M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, J. Comput. Appl. Math., 225 (2009), 20-30
##[15]
X.-L. Qin, Y. J. Cho, S. M. Kang, On hybrid projection methods for asymptotically quasi-\(\phi\)-nonexpansive mappings, Appl. Math. Comput., 215 (2010), 3874-3883
##[16]
R. T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pacific J. Math., 33 (1970), 209-216
##[17]
T. V. Su, T. V. Dinh, On the existence of solutions of quasi-equilibrium problems (UPQEP), (LPQEP), (UWQEP) and (LWQEP) and related problems, Commun. Optim. Theory, 2016 (2016), 1-21
##[18]
W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70 (2009), 45-57
##[19]
Q.-N. Zhang, Nonlinear operators, equilibrium problems and monotone projection algorithms, Commun. Optim. Theory, 2017 (2017), 1-11
##[20]
J. Zhao, Approximation of solutions to an equilibrium problem in a nonuniformly smooth Banach space, J. Inequal. Appl., 2013 (2013), 1-10
]
Inviscid incompressible limit for the strong stratified flow of a chemically reacting gaseous mixture
Inviscid incompressible limit for the strong stratified flow of a chemically reacting gaseous mixture
en
en
The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. In this paper we
study the inviscid incompressible limit for the strong stratified flow of chemically reacting gaseous mixture with the ill-prepared
initial data in the whole space.
2837
2847
Young-Sam
Kwon
Department of Mathematics
Dong-A University
Korea
ykwon@dau.ac.kr
Inviscid incompressible limit.
Article.49.pdf
[
[1]
D. Donatelli, K. Trivisa, On the motion of a viscous compressible radiative-reacting gas, Comm. Math. Phys., 265 (2006), 463-491
##[2]
D. Donatelli, K. Trivisa, A multidimensional model for the combustion of compressible fluids, Arch. Ration. Mech. Anal., 185 (2007), 379-408
##[3]
D. Donatelli, K. Trivisa, From the dynamics of gaseous stars to the incompressible Euler equations, J. Differential Equations, 245 (2008), 1356-1385
##[4]
E. Feireisl, B. J. Jin, A. Novotný, Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system, J. Math. Fluid Mech., 14 (2012), 717-730
##[5]
E. Feireisl, B. J. Jin, A. Novotný, Inviscid incompressible limits of strongly stratified fluids, Asymptot. Anal., 89 (2014), 307-329
##[6]
E. Feireisl, A. Novotný, Inviscid incompressible limits of the full Navier-Stokes-Fourier system, Comm. Math. Phys., 321 (2013), 605-628
##[7]
E. Feireisl, H. Petzeltová, Low Mach number asymptotics for reacting compressible fluid flows, Discrete Contin. Dyn. Syst., 26 (2010), 455-480
##[8]
S. Jiang, Q.-C. Ju, F.-C. Li, Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions, Comm. Math. Phys., 297 (2010), 371-400
##[9]
S. Jiang, Q.-C. Ju, F.-C. Li, Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients, SIAM J. Math. Anal., 42 (2010), 2539-2553
##[10]
S. Jiang, Q.-C. Ju, F.-C. Li, Z.-P. Xin, Low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data, Adv. Math., 259 (2014), 384-420
##[11]
N. Masmoudi, Incompressible, inviscid limit of the compressible Navier-Stokes system, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18 (2001), 199-224
]
Gohberg-Semencul type formula and application for the inverse of a conjugate-Toeplitz matrix involving imaginary circulant matrices
Gohberg-Semencul type formula and application for the inverse of a conjugate-Toeplitz matrix involving imaginary circulant matrices
en
en
Gohberg-Semencul type inverse formula of conjugate-Toeplitz (CT) is obtained by constructing a kind of imaginary cyclic
displacement transform. The stability of decomposition formula of inverse is investigated, and its algorithm is also given.
Numerical example is provided to verify the feasibility of the inverse formula. How the analogue of our formula leads to a more
efficient way to solve the conjugate-Toeplitz linear system of equations is proposed. The corresponding inverse, stability, and
algorithm of conjugate-Hankel (CH) matrix are also considered.
2848
2859
Xiaoyu
Jiang
Dept. of Information and Telecommunications Engineering
The University of Suwon
Korea
jxy19890422@sina.com
Kicheon
Hong
Dept. of Information and Telecommunications Engineering
The University of Suwon
Korea
Kchong@suwon.ac.kr
Conjugate-Toeplitz matrix
conjugate-Hankel matrix
stability
imaginary cyclic displacement
fast Fourier transform.
Article.50.pdf
[
[1]
G. Ammar, P. Gader, A variant of the Gohberg-Semencul formula involving circulant matrices, SIAM J. Matrix Anal. Appl., 12 (1991), 534-540
##[2]
G. S. Ammar, W. B. Gragg, The generalized Schur algorithm for the superfast solution of Toeplitz systems, Rational approximation and applications in mathematics and physics, Łancut, (1985), Lecture Notes in Math., Springer, Berlin, 1237 (1987), 315-330
##[3]
G. S. Ammar, W. B. Gragg, Superfast solution of real positive definite Toeplitz systems, SIAM Conference on Linear Algebra in Signals, Systems, and Control, Boston, Mass., (1986), SIAM J. Matrix Anal. Appl., 9 (1988), 61-76
##[4]
S. Barnett, M. J. C. Gover, Some extensions of Hankel and Toeplitz matrices, Linear and Multilinear Algebra, 14 (1983), 45-65
##[5]
M. I. Español, M. E. Kilmer, Multilevel approach for signal restoration problems with Toeplitz matrices, SIAM J. Sci. Comput., 32 (2010), 299-319
##[6]
I. C. Gohberg, A. A. Semencul, The inversion of finite Toeplitz matrices and their continual analogues, (Russian) Mat. Issled., 7 (1972), 201-233
##[7]
M. J. C. Gover, S. Barnett, Generating polynomials for matrices with Toeplitz or conjugate-Toeplitz inverses, Linear Algebra Appl., 61 (1984), 253-275
##[8]
M. J. C. Gover, S. Barnett, Inversion of certain extensions of Toeplitz matrices, J. Math. Anal. Appl., 100 (1984), 339-353
##[9]
M. J. C. Gover, S. Barnett, Characterisation and properties of r-Toeplitz matrices, J. Math. Anal. Appl., 123 (1987), 297-305
##[10]
M. H. Gutknecht, M. Hochbruck, The stability of inversion formulas for Toeplitz matrices, Special issue honoring Miroslav Fiedler and Vlastimil Pták, Linear Algebra Appl., 223/224 (1995), 307-324
##[11]
J. R. Jain, An efficient algorithm for a large Toeplitz set of linear equations, IEEE Trans. Acoust. Speech Signal Process., 27 (1979), 612-615
##[12]
Z.-L. Jiang, J.-X. Chen, The explicit inverse of nonsingular conjugate-Toeplitz and conjugate-Hankel matrices, J. Appl. Math. Comput., 53 (2017), 1-16
##[13]
Z.-L. Jiang, X.-T. Chen, J.-M. Wang, The explicit inverses of CUPL-Toeplitz and CUPL-Hankel matrices, East Asian J. Appl. Math., 7 (2017), 38-54
##[14]
X.-Y. Jiang, K.-C. Hong, Equalities and inequalities for norms of block imaginary circulant operator matrices, Abstr. Appl. Anal., 2015 (2015), 1-5
##[15]
X.-Y. Jiang, K.-C. Hong, Skew cyclic displacements and inversions of two innovative patterned Matrices, Appl. Math. Comput., 308 (2017), 174-184
##[16]
Z.-L. Jiang, Y.-C. Qiao, S.-D. Wang, Norm equalities and inequalities for three circulant operator matrices, Acta Math. Sin. (Engl. Ser.), 33 (2017), 571-590
##[17]
Z.-L. Jiang, T.-Y. Tam, Y.-F. Wang, Inversion of conjugate-Toeplitz matrices and conjugate-Hankel matrices, Linear Multilinear Algebra, 65 (2017), 256-268
##[18]
Z.-L. Jiang, D.-D. Wang, Explicit group inverse of an innovative patterned matrix, Appl. Math. Comput., 274 (2016), 220-228
##[19]
Z.-L. Jiang, H.-X. Xin, H.-W. Wang, On computing of positive integer powers for r-circulant matrices, Appl. Math. Comput., 265 (2015), 409-413
##[20]
Z.-L. Jiang, T.-T. Xu, Norm estimates of \(\omega\)-circulant operator matrices and isomorphic operators for \(\omega\)-circulant algebra, Sci. China Math., 59 (2016), 351-366
##[21]
Z.-L. Jiang, Z.-X. Zhou, Circulant matrices, Chengdu Technology University Publishing Company, Chengdu (1999)
##[22]
N. T. Keliba, D. Huylebrouck, A note on conjugate Toeplitz matrices, Linear Algebra Appl., 139 (1990), 103-109
##[23]
L. Lerer, M. Tismenetsky, Generalized Bezoutian and the inversion problem for block matrices, I, General scheme, Integral Equations Operator Theory, 9 (1986), 790-819
##[24]
X.-G. Lv, T.-Z. Huang, A note on inversion of Toeplitz matrices, Appl. Math. Lett., 20 (2007), 1189-1193
##[25]
J.-S. Mei, R.-Q. Wang, Eigenvalue analysis of circulant matrices extended from the Toeplitz matrices, Prog. Geophys., 28 (2013), 265-269
##[26]
M. K. Ng, Iterative methods for Toeplitz systems, Numerical Mathematics and Scientific Computation, Oxford University Press, New York (2004)
##[27]
M. K. Ng, J.-Y. Pan, Weighted Toeplitz regularized least squares computation for image restoration, SIAM J. Sci. Comput., 36 (2014), 1-94
##[28]
F. J. Simois, J. I. Acha, A new algorithm for real data convolutions with j-circulants, IEEE Signal Process. Lett., 18 (2011), 655-658
##[29]
W. F. Trench, An algorithm for the inversion of finite Toeplitz matrices, J. Soc. Indust. Appl. Math., 12 (1964), 515-522
##[30]
Y.-W. Wen, M. K. Ng, W.-K. Ching, H. Liu, A note on the stability of Toeplitz matrix inversion formulas, Appl. Math. Lett., 17 (2004), 903-907
##[31]
P.-P. Xie, Y.-M. Wei, The stability of formula of the Gohberg-Semencul-Trench type for Moore-Penrose and group inverses of Toeplitz matrices, Linear Algebra Appl., 498 (2016), 117-135
]