Existence results for equilibrium problem

TL;DR

This paper introduces a regularization approach for bifunctions in equilibrium problems, demonstrating solution set equivalence and establishing new existence results for solutions.

Contribution

It proposes a novel regularization method for bifunctions and proves the equivalence of solution sets, along with new existence theorems for equilibrium problem solutions.

Findings

Regularization of bifunctions preserves solution sets.

Equilibrium problems and their regularizations are solution-equivalent.

New existence results for equilibrium problem solutions.

Abstract

In this work, we introduce the notion of regularization of bifunctions in a similar way as the well- known convex, quasiconvex and lower semicontinuous regularizations due to Crouzeix. We show that the Equilibrium Problems associated to bifunctions and their regularizations are equivalent in the sense of having the same solution set. Also, we present new results of existence of solutions for Equilibrium Problems.