Approximating a Zero of Sum of Two Monotone Operators Which Solves a Fixed Point Problem in Reflexive Banach Spaces. (17th February 2020)

• Record Type: Journal Article
• Authors: Ogbuisi, Ferdinard Udochukwu; Izuchukwu, Chinedu
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 3(2020)
• Page Start: 322
• Page End: 343
• Publication Date: 2020-02-17
• Subjects: Anti-resolvent operators -- Bregman inverse strongly monotone -- Bregman strongly nonexpansive mapping -- fixed point problem -- maximal monotone mapping -- monotone variational inclusion problem -- resolvent operators; 47H09 -- 47H10 -- 49J20 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1628050
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The purpose of this paper is to introduce an iterative method for approximating a point in the set of zeros of the sum of two monotone mappings, which is also a solution of a fixed point problem for a Bregman strongly nonexpansive mapping in a real reflexive Banach space. With our iterative technique, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a variational inclusion problem for sum of two monotone mappings and the set of solutions of a fixed point problem for Bregman strongly nonexpansive mapping. We give applications of our result to convex minimization problem, convex feasibility problem, variational inequality problem, and equilibrium problem. Our result complements and extends some recent results in literature.