Shrinking projection method for solving inclusion problem and fixed point problem in reflexive Banach spaces. (2nd September 2021)

• Record Type: Journal Article
• Authors: Chang, Shih-sen; Yao, J. C.; Wen, Ching-Feng; Qin, Li Juan
• Is Part Of: Optimization. Volume 70:Number 9(2021)
• Page Start: 1921
• Page End: 1936
• Publication Date: 2021-09-02
• Subjects: Bregman distance -- Bregman quasi-nonexpansive mapping -- Bregman strongly nonexpansive mapping -- maximal monotone operator -- Bregman inverse strongly monotone mapping; 47H09 -- 47H10 -- 49J20 -- 49J40; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1763988
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The purpose of this paper is to find a common element in the intersection of the set of zeros of the inclusion problem of sum of two monotone mappings and the set of fixed points of a Bregman quasi nonexpansive mapping in a reflexive Banach space by using Bregman distance and shrinking projection method. Under suitable conditions, some strong convergence theorems are proved. As applications, we utilize our results to study the convex minimization problem, variational inequality problem.