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.
