Bregman strongly nonexpansive operators in reflexive Banach spaces

被引：69

作者：

Martin-Marquez, Victoria ^{[1
]}

Reich, Simeon ^{[2
]}

Sabach, Shoham ^{[2
]}

机构：

[1] Univ Seville, Dept Anal Matemat, E-41080 Seville, Spain

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 400卷 / 02期

基金：

以色列科学基金会;

关键词：

Bregman distance; Bregman strongly nonexpansive operator; Legendre function; Monotone mapping; Nonexpansive operator; Reflexive Banach space; Resolvent; Totally convex function; CONVERGENCE THEOREM; PROJECTIONS; CONVEXITY;

D O I：

10.1016/j.jmaa.2012.11.059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a detailed study of right and left Bregman strongly nonexpansive operators in reflexive Banach spaces. We analyze, in particular, compositions and convex combinations of such operators, and prove the convergence of the Picard iterative method for operators of these types. Finally, we use our results to approximate common zeros of maximal monotone mappings and solutions to convex feasibility problems. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：597 / 614

页数：18

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