In this paper, the author considers generalized minimax theorems for vector set-valued mappings using Fan-KKM theorem on nonconvex domains of Hausdorff topological vector spaces.

Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.

The aim of this article is obtain a Krasnoselskĭı cone compression theorem for multimaps in the class S-KKM.

Let us consider two nonempty subsets A, B of a normed linear space X , and let us denote by 2B the set of all subsets of B. We introduce a new class of multivalued mappings {T : A → 2B}, called R-KKM mappings, which extends the notion of KKM mappings. First, we discuss some sufficient conditions for which the set ∩{T (x) : x ∈ A} is nonempty. Using this nonempty intersection theorem, we attempt...

We obtain generalizations of the Fan’s matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.

In this communication, we establish some existence theorem for a new class of generalized mixed vector quasi-variationallike inequalities with fuzzy mappings in topological vector spaces by using the KKM-Fan Theorem and an equivalent fixed point theorem.

From the KKM theorem for the “closed” and “open” valued cases, we deduce a generalization of the Alexandroff–Pasynkoff theorem, existence theorems for almost fixed points of lower semicontinuous multimaps, and a partial solution of the Ben-El-Mechaiekh conjecture.

In hyperconvex metric spaces, we introduce Knaster-KuratowskiMazurkiewicz mappings (in short KKM-maps). Then we prove an analogue to Ky Fan fixed point theorem in hyperconvex metric spaces.