Comments on the KKM theory on hyperconvex metric spaces

Recent results in the KKM theory on abstract convex spaces and the related multimap classes $\frak{KC}$ and $\frak{KO}$ are applied to deduce generalizations of results on KKM maps in metric spaces in Amini et al. [1] and generalized KKM theorems on hyperconvex metric spaces in Chang et al. [4, 5].

Remarks on Weakly KKM Maps in Abstract Convex Spaces

A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones inG-convex spaces andϕA-spaces(X,D;{ϕA}A∈〈D〉). Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized and unified.