OPTIMALITY CONDITIONS FOR SOLVING NONCONVEX SET-VALUED EQUILIBRIUM PROBLEMS

Abstract

In this paper, sufficient conditions ensuring the existence of solutions for set-valued equilibrium problems are obtained. The convexity assumption on the whole domain is not necessary and just the closure of a quasi-self-segment-dense subset of the domain is convex. Using a KKM theorem and a notion of Q-selected preserving $R_{-}^{*}$-intersection($R_{-}^{*}$-inclusion) for set-valued mapping, the existence results are proved in real Hausdorff topological vector spaces.