KKM lemmas and minimax inequality theorems in abstract convexity spaces

摘要

The purpose of this paper is to give some further results in a type of generalized convexity spaces. First, we prove that an abstract convex space has KKM property if and only if it has a strong Fan-Browder property. Then we introduce an abstract convex structure via an upper semi-continuous multi-valued mapping and establish some generalized versions of KKM lemma. By employing our general KKM lemmas, we derive some generalizations of minimax inequalities, which contain several existing ones as special cases.