A strong convergence theorem for solving an equilibrium problem and a fixed point problem using the Bregman distance

TL;DR

This paper introduces a new Bregman distance-based algorithm for finding common solutions to equilibrium and fixed point problems, proving its strong convergence and demonstrating its effectiveness through numerical examples.

Contribution

It presents a novel projection-type algorithm using Bregman distance with proven strong convergence for solving combined equilibrium and fixed point problems.

Findings

Algorithm converges strongly under certain conditions

Numerical example confirms convergence performance

Method effectively finds common solutions

Abstract

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence generated by the algorithm will be established under suitable conditions. Finally, using MATLAB software, we present a numerical example to illustrate the convergence performance of our algorithm.