Approximating Common Fixed Points of Bregman Weakly Relatively Nonexpansive Mappings in Banach Spaces. (3rd February 2014)

• Record Type: Journal Article
• Authors: Pang, Chin-Tzong; Naraghirad, Eskandar
• Other Names: Alber Yakov Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-02-03
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/743279
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Using Bregman functions, we introduce a new hybrid iterative scheme for finding common fixed points of an infinite family of Bregman weakly relatively nonexpansive mappings in Banach spaces. We prove a strong convergence theorem for the sequence produced by the method. No closedness assumption is imposed on a mappingT : C → C, whereC is a closed and convex subset of a reflexive Banach spaceE . Furthermore, we apply our method to solve a system of equilibrium problems in reflexive Banach spaces. Some application of our results to the problem of finding a minimizer of a continuously Fréchet differentiable and convex function in a Banach space is presented. Our results improve and generalize many known results in the current literature.