Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings

Abstract

Let $K$ be a nonempty compact convex subset of a topological vector space. In this paper-sufficient conditions are given for the existence of $x\in K$ such that $F(T)\cap \text{V}\text{E}\text{P}(F)\ne \varnothing$, where $F(T)$ is the set of all fixed points of the multivalued mapping $T$ and $\text{VEP}(F)$ is the set of all solutions for vector equilibrium problem of the vector-valued mapping $F$. This leads us to generalize and improve some existence results in the recent references.