Well-posedness of Systems of Equilibrium Problems

Abstract

In this paper we introduce the concepts of well-posedness and generalized well-posedness for a system of equilibrium problems. We derive a metric characterization of well-posedness by considering the diameter of approximating solution set and a Furi-Vignoli type characterization of generalized well-posedness by considering the Kuratowski noncompactness measure of approximating solution set. Under suitable conditions, we prove that the well-posedness of a system of equilibrium problems is equivalent to the existence and uniqueness of its solution.