REMARKS ON ABSTRACT CONVEXITY SPACES OF XIANG ET AL.

Abstract

Xiang, Xia and Chen in 2013 [12] introduced an abstract convexity structure via an upper semicontinuous multi-valued map and established some generalized versions of the KKM lemma. By employing these general KKM lemmas, they derived some generalizations of minimax inequalities. Our aim in the present article is, as in our previous one [4], to show that most results in [12] are either consequences of known ones or can be stated in more general forms in the frame of abstract convex spaces in the sense of Park.