International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 423596, 10 pages
doi:10.1155/2008/423596

Remarks on weakly KKM maps in abstract convex spaces

Abstract

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 in G-convex spaces and ϕA-spaces (X,D;{ϕA}A∈〈D〉). Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized and unified.