Convergence of Solutions to Lexicographic Equilibrium Problems

Abstract

This article deals with lexicographic equilibrium problems on Banach spaces. We first study the existence of solutions for such problems. Then, we investigate the Painlevé-Kuratowski convergence of the solution sets for a family of perturbed problems in a such way that they are perturbed by sequences constrained sets and objective functions converging. Several illustrative examples are given which clarify the essentialness of imposed assumptions. As an application, we discuss various results on the Painlevé-Kuratowski convergence for lexicographic variational inequalities.