扩展到无弱序列连续对偶映射Banach空间的关于变分包含与不动点问题的广义迭代算法

Abstract

Abstract: In this paper, we introduce an iterative scheme by the general iterative method for finding a common element of the set of solutions of a general system of nonlinear variational inclusions for two H-accretive mappings and the set of common fixed points of an infinite family of strictly pseudo-contractive mappings which solves some variational inequality in q-uniformly smooth Banach spaces without the weakly sequentially continuous duality mapping. Our results improve and extend the corresponding results announced by many others.

Key words: H-Accretive mapping, Variational inclusion, Strictly pseudo-contractive mapping, Inverse-strongly-accretive mapping, Sunny nonexpansive retraction

CLC Number:

O177.91

Liu Ying. The General Iterative Algorithms for Variational Inclusions and Fixed Point Problems Extended to Banach Spaces Without the Weakly Sequentially Continuous Duality Mapping[J].Acta mathematica scientia,Series A, 2018, 38(2): 244-263.

Trendmd

References

[1] Liu Y. Strong convergence theorems for variational inclusion problems and strict pseudo-contractions in Hilbert spaces. Nonlinear Functional Analysis and Applications, 2012, 17:421-432
[2] Xu H K. Viscosity approximation methods for nonexpansive mappings. J Math Anal Appl, 2004, 298:279-291
[3] Liu Y, Chen Y. Viscosity iteration algorithms for nonlinear variational inclusions and fixed point problems in Banach spaces. J Appl Math Comput, 2014, 45:165-181
[4] Marino G, Xu H K. A general iterative method for nonexpansive mappings in Hilbert spaces. J Math Anal Appl, 2006, 318:43-52
[5] Cho Y J, Kang S M, Qin X. Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces. Comput Math Appl, 2008, 56:2058-2064
[6] Qin X, Cho, Y J, Kang J I, et al. Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces. J Comput Anal Appl, 2009, 230(1):121-127
[7] Yao Y, Liou Y C, Kang S M. Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings. Appl Math Comput, 2009, 208:211-218
[8] Sunthrayuth P, Kuman P. Iterative methods for variational inequality problems and fixed point problems of a countable family of strict pseudo-contractions in a q-uniformly smooth Banach space. Fixed Point Theory and Applications, 2012, 2012:65
[9] Ceng L C, Ansari Q H, Yao J C. Some iterative methods for finding fixed points and for solving constrained convex minimization problems. Nonlinear Anal, 2011, 74:5286-5302
[10] Fang Y P, Huang N J. H-Accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces. Applied Mathematics Letters, 2004, 17:647-653
[11] Liu S, He H. Approximating solution of 0∈ Tx for an H-accretive operator in Banach spaces. J Math Anal Appl, 2012, 385:466-476
[12] Kazmi K R, Bhat M I. Iterative algorithm for a system of nonlinear variational-like inclusions. Computers and Mathematics with Applications, 2004, 48:1929-1935
[13] Noor M A, Noor K I. Resolvent methods for solving system of general variational inclusions. J Optim Theory Appl, 2011, 148:422-430
[14] Lou J, He X F, He Z. Iterative methods for solving a system of variational inclusions involving H-η-monotone operators in Banach spaces. Computers and Mathematics with Applications, 2008, 55:1832-1841
[15] Fang Y P, Huang N J. A new system of variational inclusions with monotone operators in Hilbert spaces. Comput Math Appl, 2005, 49:365-374
[16] Zou Y Z, Huang N J. A new system of variational inclusions involving H(·,·)-accretive operator in Banach spaces. Applied Mathematics and Computation, 2009, 212:135-144
[17] Qin X, Chang S S, Cho Y J, et al. Approximation of solutions to a system of variational inclusions in Banach spaces. J Inequa Appl, 2010, Article ID:916806
[18] Pei Y G, Liu F, Gao Q. Strong convergence of strict pseudo-contractions in q-uniformly smooth Banach spaces. J Appl Math Informatics, 2015, 33(1):13-31
[19] Cai G, Bu S. Modified extragradient methods for variational inequality problems and fixed point problems for an infinite family of nonexpansive mappings in Banach spaces. J Glob Optim, 2013, 55:437-457
[20] Moudafi A. Viscosity approximation methods for fixed point problems. J Math Anal Appl, 2000, 241:46-55
[21] Qin X, Cho S Y, Kang S M. Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications. Journal of Computational and Applied Mathematics, 2009, 233:231-240
[22] He X, Xu Y, He Z. Iterative approximation for a zero of accretive operator and fixed points problems in Banach spaces. Applied Mathematics and Computation, 2011, 217:4620-4626
[23] Xu H K. Iterative algorithms for nonlinear operators. J London Math Soc, 2002, 66:240-256
[24] Zhang H, Su Y F. Strong convergence theorems for strict pseudo-contractions in quniformly smooth Banach spaces. Nonlinear Anal, 2009, 70:3236-3242
[25] Bruck R E. Properties of fixed point sets of nonexpansive mappings in Banach spaces. Tras Amer Math Soc, 1973, 179:251-262
[26] Yao Y H, Noor M A, Noor K I, et al. Modified extragradient methods for a system of variational inequalities in Banach spaces. Acta Appl Math, 2010, 110:1211-1224

The General Iterative Algorithms for Variational Inclusions and Fixed Point Problems Extended to Banach Spaces Without the Weakly Sequentially Continuous Duality Mapping

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 3

Metrics

Comments

Recommended 10

[1]	Chang Shih-sen, Liu Zhenhai, Wen Ching-Feng, Tang Jinfang. Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem [J]. Acta mathematica scientia,Series A, 2018, 38(2): 231-243.
[2]	DENG Wei-Qi. Viscosity Method for Hierarchical Fixed Point Approach to Hierarchical Variational Inclusion Problems [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1254-1263.
[3]	GU Feng. On the Ishikawa Iterative Approximation with Mixed Errors for Solutions to Variational Inclusions with Strongly Accretive Type Mappings in Banach Spaces [J]. Acta mathematica scientia,Series A, 2005, 25(2): 176-181.