Strong Convergence Theorems for Bregman Demigeneralized Mappings in Banach Spaces with Applications. (25th April 2020)

• Record Type: Journal Article
• Authors: Gazmeh, Hamid; Naraghirad, Eskandar
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 6(2020)
• Page Start: 730
• Page End: 757
• Publication Date: 2020-04-25
• Subjects: Bregman function -- uniformly convex function -- uniformly smooth function -- fixed point -- strong convergence -- Bregman (β, γ)-demigeneralized mapping; 47H10 -- 37C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1673773
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we first introduce a new class of mappings called Bregman ( β, γ ) -demigeneralized mappings in a Banach space E . Then, using Bregman projection method, we prove a convergence theorem for finding a common fixed point of a family of the new mappings in a Banach space E . Furthermore, we apply our method to prove strong convergence theorems of iterative schemes for finding common fixed points of infinitely many nonlinear mappings satisfying the jointly demiclosedness principle in a Banach space E . Our new technique is based on the strong coerciveness of a Bregman function and the method of proof is completely different from those available in the literature. Some application of our results to the solution of common zeros of maximal monotone operators is presented. Finally, an illustrative numerical example is presented. Our results improve and generalize many known results in the current literature.