On hemicontinuity of bifunctions for solving equilibrium problems

Abstract

This paper deals with solving equilibrium problems under local conditions on equilibrium bifunctions. Some techniques first considered for multivalued mixed variational inequalities are investigated and applied to equilibrium problems. It results that the notion of hemicontinuity is not needed on the whole space when solving equilibrium problems involving pseudomonotone or quasimonotone bifunctions. Generalizations of some well-known results concerning existence of solutions of equilibrium problems are obtained and applications to equilibrium problems involving two, rather than one, bifunctions are given.

Keywords

• equilibrium problem
• variational inequality problem
• multivalued mapping
• hemicontinuity
• pseudomonotonicity
• quasimonotonicity
• 65k10
• 90c33
• 91b50