Abstract convexity and generalizations of Himmelberg type fixed-point theorems

In this paper, we study a class KKM(X, Y) of set-valued mappings with KKM property in L-convex spaces introduced by Ben-El-Mechaiekh et al. Several new Himmelberg type fixed-point theorem for mappings with KKM property are established in noncompact locally L-convex spaces. These theorems improve, unify, and generalize many known results in the literatures.