Generalized KKM theorem and variational inequalities

Abstract

The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general versions of the famous KKM theorem, Ky Fan's minimax inequality, and the Browder-Hartman-Stampacchia variational inequality theorem. As applications we utilize these results to study the saddle point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results presented in this paper extend and improve some recent results of other authors.