# Convergence results for a common solution of a finite family of equilibrium problems and quasi-Bregman nonexpansive mappings in Banach space

## TL;DR

This paper introduces an iterative method to find a common fixed point of multiple quasi-Bregman nonexpansive mappings in Banach spaces, which also solves a related equilibrium problem.

## Contribution

It proposes a new iterative process that guarantees convergence to a common solution for a finite family of mappings and equilibrium problems in Banach spaces.

## Key findings

- Convergence of the iterative process is established.
- The method finds a unique solution to the equilibrium problem.
- Applicable to a broad class of mappings in Banach spaces.

## Abstract

We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.