In this paper, we introduce a new class of set-valued vector implicit quasi complementarity problemswith corresponding set-valued implicit quasi variational inequality problems. By means of the Fan–KKM theorem, we investigate the nonemptiness and compactness of solution sets of these problems. Our work generalizes and improves some results appeared recently in the literature. © 2011 Elsevier Lt...

The solvability of the generalized weak vector implicit variational inequality problem, generalized strong vector implicit variational inequality problem and generalized vector variational inequality problem are proved by using a generalized Fan’s KKM theorem. Our results extend and unify corresponding results of other authors.

In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

This paper presents new random fixed point theorems and random Leray–Schauder alternatives for a variety of maps (e.g., Bκ, Uκ c , KKM and PK maps). A random Kransnoselskii cone compression theorem for Uκ c maps is also given. Various random approximation theorems for the above classes are proved and as applications several random fixed point theorems are also derived.

A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones in G-convex spaces and φA-spaces X,D; {φA}A∈〈D〉 . Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized an...