Existence solutions of vector equilibrium problems and fixed point of multivalued mappings (Q1949536)

Summary: 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 \(F(T) \cap \text{VEP}(F) \neq \emptyset\), 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 literature.