A New Shrinking projection Algorithm for an infinite family of Bregman weak relatively nonexpansive mappings in a Banach Space

TL;DR

This paper introduces a novel shrinking projection algorithm that ensures strong convergence to common solutions involving Bregman mappings, maximal monotone operators, and equilibrium problems in Banach spaces.

Contribution

It proposes a new shrinking projection method utilizing generalized resolvents and projections for convergence in complex Banach space problems.

Findings

Establishes strong convergence of the proposed algorithm.

Unifies fixed point and equilibrium problem solutions.

Applicable to infinite families of Bregman weak relatively nonexpansive mappings.

Abstract

In this paper, using a new shrinking projection method and generalized resolvents of maximal monotone operators and generalized projections, we consider the strong convergence for finding a common point of the fixed points of a Bregman quasi-nonexpansive mapping, and common fixed points of a infinite family of Bregman weak relatively nonexpansive mappings, and common zero points of a finite family of maximal monotone mappings, and common solutions of an equilibrium problem in a reflexive Banach space.