In this paper, we introduced the generalized vector variational inequality-type problem and the generalized vector complementarity-type problem in the setting of topological vector space. By utilizing a modified version of the Fan–KKM theorem, we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption. Further, we prove that...

The aim of this paper is to establish the existence of at least one solution for a general inequality of quasi-hemivariational type, whose solution is sought in a subset K of a real Banach space E . First, we prove the existence of solutions in the case of compact convex subsets and the case of bounded closed and convex subsets. Finally, the case when K is the whole space is analyzed and necess...

In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general s...

In this paper, by introducing some new concepts in minimal spaces, we prove a generalized form of the Fan-KKM theorem vector spaces. A class F-implicit variational inequality problems and, as an application is investigated. Moreover, existence for kind under suitable assumptions spaces given.

In this paper, we establish some existence results for strong vector equilibrium problems (for short, SVEP) in topological vector spaces. The solvability of the SVEP is presented using the The second author was in part supported by a grant from IPM (No. 85470015) 220 A.P. Farajzadeh et. al. CUBO 12, 1 (2010) Fan-KKM lemma. These results give a positive answer to an open problem proposed by Chen...

In this paper we consider stochastic equilibrium problems involving parameter of probability measures. Employing the fixed point theorem Knaster, Kuratowski, Mazurkiewicz, and Fan (KKM-Fan), conditions for existence solutions to such are established. We then propose new metric concepts on underlying spaces study some properties corresponding these metrics. Afterwards, sufficient solution mappin...

Various types of φA-spaces (X,D; {φA}A∈〈D〉) are simply G-convex spaces. Various types of generalized KKM maps on φA-spaces are simply KKM maps on G-convex spaces. Therefore, our G-convex space theory can be applied to various types of φAspaces. As such examples, we obtain KKM type theorems and a very general fixed point theorem on φA-spaces. RESUMEN Varios tipos de φA-espacios (X,D; {φA}A∈〈D〉) ...

In this paper, we consider mixed vector variational-like inequality problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued mappings. Further, by exploiting KKM-Fan lemma, we establish some existence results for solutions of mixed vector variational-like inequality problems and show that the solution sets of these problems are compact.

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.

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.