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.

In 1929, the KKMmap was introduced by Knaster et al. [13] and it provides the foundation for many well-known existence results, such as Ky Fan’s minimax inequality theorem, Ky Fan-Browder’s fixed point theorem, Nash’s equilibrium theorem, HartmanStampacchia’s variational inequality theorem and many others (see [1, 2, 5–12, 14–17]). The central idea of applying KKM theory to prove that a family ...