THE KKM, MATCHING, AND FIXED POINT THEOREMS IN GENERALIZED CONVEX SPACES

Abstract

From our version of the KKM theorem for G-convex spaces, we deduce generalizations of the intersection theorems of Sperner [40] and Alexan-droff-Pasynkoff [1], matching theorems of Lassonde [17] and Klee [14], and various forms of the Fan-Browder type fixed point theorems. Applications to the existence of maximal elements and approximate fixed points are added.