Existence of common fixed points using Bregman nonexpansive retracts and Bregman functions in Banach spaces

Abstract

In this paper, we first introduce the concepts of Bregman nonexpansive retract and Bregman one-local retract and then use these concepts to establish the existence of common fixed points for Banach operator pairs in the framework of reflexive Banach spaces. No compactness assumption is imposed either on C or on T, where C is a closed and convex subset of a reflexive Banach space E and T : C → C is a Bregman nonexpansive mapping. We also establish the well-known De Marr theorem for a Banach operator family of Bregman nonexpansive mappings. © 2013 Hussain et al.; licensee Springer.