Convergence Theorems for Equilibrium and Fixed Point Problems

被引：0
作者：
Yekini Shehu
机构：
[1] University of Nigeria,Department of Mathematics
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2016年 / 39卷
关键词：
Left Bregman strongly relatively nonexpansive mapping; Left Bregman projection; Equilibrium problem; Banach spaces; 47H06; 47H09; 47J05; 47J25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Our purpose in this paper is to prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.
引用
收藏
页码：133 / 153
页数：20
相关论文
共 89 条
  • [11] Bauschke HH(1997)Iterative averaging of entropic projections for solving stochastic convex feasibility problems Comput. Optim. Appl. 8 21-39
  • [12] Borwein JM(2013)Strong convergence theorems for variational inequality problems and fixed point problems in Banach spaces Bull. Malays. Math. Sci. Soc. 36 525-540
  • [13] Combettes PL(1981)An iterative row-action method for interval convex programming J. Optim. Theory Appl. 34 321-353
  • [14] Bello Cruz JY(1996)Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization Optimization 37 323-339
  • [15] Iusem AN(2013)Strong convergence theorems for equilibrium problems and weak Bregman relatively nonexpansive mappings in Banach spaces J. Inequal. Appl. 2013 119-23
  • [16] Blum E(2011)Approximation of fixed points of weak Bregman relatively nonexpansive mappings in Banach spaces Int. J. Math. Math. Sci. 2011 1-136
  • [17] Oettli W(2005)Equilibrium programming in Hilbert spaces J. Nonlinear Convex Anal. 6 117-112
  • [18] Borwein JM(2011)Zero theorems of accretive operators Bull. Malays. Math. Sci. Soc. 34 103-523
  • [19] Reich S(2005)Proximal point algorithms with Bregman functions in Banach spaces J. Nonlinear Convex Anal. 6 505-280
  • [20] Sabach S(2009)A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping J. Appl. Math. Comput. 29 263-912
123456789