Strong Convergence Theorems for a Countable Family of Multi-Valued Bregman Quasi-Nonexpansive Mappings in Reflexive Banach Spaces. (4th May 2017)

• Record Type: Journal Article
• Authors: Chang, S. S.; Wang, X. R.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 5(2017)
• Page Start: 575
• Page End: 589
• Publication Date: 2017-05-04
• Subjects: Bregman distance -- Bregman projection -- Legendre function -- multi-valued Bregman quasi-nonexpansive mapping -- totally convex function; 47J05 -- 47H09 -- 49J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1252392
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: This article uses the shrinking projection method introduced by Takahashi, Kubota and Takeuchi to propose an iteration algorithm for a countable family of Bregman multi-valued quasi-nonexpansive mappings in order to have the strong convergence under a limit condition in the framework of reflexive Banach spaces. We apply our results to a zero point problem of maximal monotone mappings and equilibrium problems in reflexive Banach spaces. The results presented in the article improve and extend the corresponding results of that found in the literature.