A novel hybrid method for equilibrium problems and fixed point problems

TL;DR

This paper introduces a new hybrid algorithm that efficiently solves equilibrium and fixed point problems by using cutting-halfspaces, requiring only an optimization step per iteration, with proven convergence and numerical validation.

Contribution

It presents a novel hybrid method that simplifies the solution process for equilibrium and fixed point problems, avoiding extra steps used in previous methods.

Findings

Proves strong convergence of the proposed method.

Demonstrates effectiveness through numerical examples.

Reduces computational complexity by solving only one optimization problem per iteration.

Abstract

The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the extra-steps as in some previously known methods. The strongly convergence theorem is established and some numerical examples are presented to illustrate its convergence.