Solving Equilibrium Problems with Bifunctions Having the Property of Negative Transitivity

Abstract

In this article, we introduce the notion of bifunction with the property of negative transitivity and, using the Berge-Klee intersection theorem, we establish existence theorems of the solutions for the equilibrium problems, when the involved bifunction has this property. Then, using standard scalarization techniques, we obtain existence criteria of the solutions for vector equilibrium problems. The last section of the article is devoted to the scalar and vector quasi-equilibrium problems.