APPLICATIONS OF THE KKM PRINCIPLE ON ABSTRACT CONVEX MINIMAL SPACES

Abstract

We introduce a new concept of abstract convex minimal spaces which is used to establish typical results in the KKM theory. Since any minimal space can be made into a topological space, results on abstract convex minimal spaces can be deduced from the theory on abstract convex spaces. In this way, the KKM type theorems are used to obtain coincidence theorems, the Fan-Browder type fixed point theorems, the Fan intersection theorem, and the Nash equilibrium theorem on abstract convex minimal spaces.