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
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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.
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页码:133 / 153
页数:20
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  • [21] Bregman LM(2008)Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization Set-Valued Anal. 16 899-5465
  • [22] Butnariu D(2012)Right Bregman nonexpansive operators in Banach spaces Nonlinear Anal. 75 5448-1063
  • [23] Resmerita E(2012)Iterative methods for approximating fixed points of Bregman nonexpansive operators Discret. Contin. Dyn. Syst. 6 1043-1130
  • [24] Butnariu D(1964)Sur la fonction polaire dune fonction semi-continue superieurement C. R. Acad. Sci. Paris 258 1128-456
  • [25] Censor Y(2010)A partial complement method for approximating solutions of a primal dual fixed-point problem Optim. Lett. 4 449-558
  • [26] Reich S(2008)A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings Appl. Math. Comput. 197 548-30
  • [27] Cai G(2009)Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces J. Comput. Appl. Math. 225 20-167
  • [28] Bu S(2010)Convergence theorems on an iterative method for variational inequality problems and fixed point problems Bull. Malays. Math. Sci. Soc. 33 155-1965
  • [29] Censor Y(2007)Strong convergence theorems for relatively nonexpansive mappings in a Banach space Nonlinear Anal. 67 1958-485
  • [30] Lent A(2009)A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces J. Nonlinear Convex Anal. 10 471-44