Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces

被引：166
|
作者：
Reich, Simeon [1 ]
Sabach, Shoham [1 ]
机构：
[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 01期
基金：
以色列科学基金会;
关键词：
Banach space; Bregman distance; Bregman firmly nonexpansive operator; Bregman inverse strongly monotone operator; Bregman projection; Bregman strongly nonexpansive operator; Convex feasibility problem; Equilibrium problem; Iterative algorithm; Legendre function; Monotone operator; Totally convex function; Variational inequality; PROJECTIONS; CONVEXITY;
D O I：
10.1016/j.na.2010.03.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the convergence of two iterative algorithms for finding common fixed points of finitely many Bregman strongly nonexpansive operators in reflexive Banach spaces. Both algorithms take into account possible computational errors. We establish two strong convergence theorems and then apply them to the solution of convex feasibility, variational inequality and equilibrium problems. (C) 2010 Elsevier Ltd. All rights reserved.
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页码：122 / 135
页数：14
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