OPTIMALITY CONDITIONS FOR SOLVING NONCONVEX SET-VALUED EQUILIBRIUM PROBLEMS

In this paper, sufficient conditions ensuring the existence of solutions for setvalued 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, existence results are established in real Hausdorff topological vector spaces.