Shrinking projection method for a sequence of relatively quasi-nonexpansive multivalued mappings and equilibrium problem in Banach spaces

TL;DR

This paper introduces a new iterative process using the Shrinking projection method to find common fixed points and solutions to equilibrium problems in Banach spaces, improving existing convergence results.

Contribution

The paper develops a novel iterative approach that extends previous methods for convergence to common fixed points and equilibrium solutions in Banach spaces.

Findings

Established strong convergence of the new iterative process.

Extended and improved previous convergence results.

Applicable to a broad class of multivalued mappings and equilibrium problems.

Abstract

Strong convergence of a new iterative process based on the Shrinking projection method to a common element of the set of common fixed points of an infinite family of relatively quasi-nonexpansive multivalued mappings and the solution set of an equilibrium problem in a Banach space is established. Our results improved and extend the corresponding results announced by many others.