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.

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.

In 1952, Ky Fan proved a combinatorial theorem generalizing the Borsuk-Ulam theorem stating that there is no Z2-equivariant map from the d-dimensional sphere S to the (d − 1)-dimensional sphere Sd−1. The aim of the present paper is to provide the same kind of combinatorial theorem for Dold's theorem, which is a generalization of the Borsuk-Ulam theorem when Z2 is replaced by Zq, and the spheres...

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...