REMARKS ON THE KKM PROPERTY FOR OPEN-VALUED MULTIMAPS ON GENERALIZED CONVEX SPACES

Abstract

Let (X, D; <TEX>${\Gamma}$</TEX>) be a G-convex space and Y a Hausdorff space. Then <TEX>$U^K_C$</TEX>(X, Y) <TEX>${\subset}$</TEX> KD(X, Y), where <TEX>$U^K_C$</TEX> is an admissible class (dup to Park) and KD denotes the class of multimaps having the KKM property for open-valued multimaps. This new result is used to obtain a KKM type theorem, matching theorems, a fixed point theorem, and a coincidence theorem.