Bregman strongly nonexpansive operators in reflexive Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:400

Article

Martin-Marquez, Victoria¹  Reich, Simeon²  Sabach, Shoham² 

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

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

关键词: Bregman distance;    Bregman strongly nonexpansive operator;    Legendre function;    Monotone mapping;    Nonexpansive operator;    Reflexive Banach space;    Resolvent;    Totally convex function;   

DOI  :  10.1016/j.jmaa.2012.11.059

来源: Elsevier

【 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.

【 授权许可】

Free