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

Remarks on Weakly KKM Maps in Abstract Convex Spaces

Sehie Park1,2

1Natural Sciences Division, The National Academy of Sciences, Seoul 137-044, South Korea
2Department of Mathematics, Seoul National University, Seoul 151-747, South Korea

Received 26 September 2007; Accepted 7 January 2008

Academic Editor: Petru Jebelean

Copyright © 2008 Sehie Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.