EXISTENCE THEOREMS FOR GENERALIZED VECTOR VARIATIONAL INEQUALITIES WITH PSEUDOMONOTONICITY AND THEIR APPLICATIONS

Abstract

The purpose of this paper is to study the solvability for a class of generalized vector variational inequalities with pseudomonotonicity in reflexive Banach spaces. Utilizing the KKM-Fan lemma and the Nadler’s result, we derive the solvability results for this class of generalized vector variational inequalities with pseudomonotonicity. Utilizing these results, we also establish some existence theorems for zero points of pseudomonotone multifunctions including the characterization of the existence of zero points.