Remarks on generalized weak KKM multimaps

Abstract

The concept of generalized KKM maps was initiated by Kassay-Kolumbán in 1990 and Chang-Zhang in 1991. Recently, Balaj and his colleagues extended generalized KKM maps w.r.t. a multimap to weak KKM maps and generalized weak KKM maps w.r.t. a multimap, and applied them to various problems in the KKM theory. However, their results are mainly concerned within the realm of topological vector spaces. Our aim in this article is to extend some of them to abstract convex spaces. Some related facts are also discussed.