Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces

Abstract

We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings.