An iterative algorithm for a common fixed point of Bregman Relatively Nonexpansive Mappings

TL;DR

This paper presents an iterative algorithm for approximating common fixed points of Bregman relatively-nonexpansive mappings in Banach spaces, with proven strong convergence and unification of existing results.

Contribution

The paper introduces a new iterative scheme for finding common fixed points of Bregman relatively-nonexpansive mappings and proves its strong convergence in reflexive Banach spaces.

Findings

Established strong convergence of the iterative scheme.

Unified various known results in the literature.

Provided conditions for convergence in reflexive Banach spaces.

Abstract

We introduce and investigate an iterative scheme for approximating common fixed point of a family of Bregman relatively-nonexpansive mappings in real reflexive Banach spaces. We prove strong convergence theorem of the sequence generated by our scheme under some appropriate conditions. Furthermore, our scheme and results unify some known results obtained in this direction.