Abstract convexity and generalizations of Himmelberg type fixed-point theorems (Q5948725)

This article deals with the class \(\text{KKM}(X,Y)\) of set-valued mappings with KKM property between two \(L\)-convex spaces \(X\) and \(Y\). The main result is a Himmelberg-type new fixed point theorem for upper semicontinuous mappings \(T\in \text{KKM}(X,D)\) with closed values in the case when \(X\) is a locally \(L\)-convex space, \(D\) an \(L\)-compact subset of \(X\). This theorem generalizes some results by T. H. Chang and C. L. Yen, G. X. Z. Yuan, X. Wu and A. Li, and others.