Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings

TL;DR

This paper introduces two new parallel hybrid algorithms to find common solutions for generalized equilibrium problems and fixed points of pseudocontractive mappings in Hilbert spaces, with proven convergence and numerical validation.

Contribution

The paper presents novel parallel hybrid methods for solving complex equilibrium and fixed point problems, with strong convergence results and practical numerical examples.

Findings

Algorithms converge strongly under standard assumptions

Numerical example demonstrates efficiency of the methods

Methods effectively handle multiple equilibrium and fixed point problems

Abstract

In this paper, we propose two novel parallel hybrid methods for finding a common element of the set of solutions of a finite family of generalized equilibrium problems for monotone bifunctions $\left\{f_i\right\}_{i=1}^N$ and $\alpha$ - inverse strongly monotone operators $\left\{A_i\right\}_{i=1}^N$ and the set of common fixed points of a finite family of (asymptotically) $\kappa$- strictly pseudocontractive mappings $\left\{S_j\right\}_{j=1}^M$ in Hilbert spaces. The strong convergence theorems are established under the standard assumptions imposed on equilibrium bifunctions and operators. A numerical example is presented to illustrate the efficiency of the proposed parallel methods.