Nonconvex Equilibrium Problems Via a KKM Theorem

Abstract

In this paper, we establish existence results for vector equilibrium problems without convexity assumptions on the whole domain, but just on the closure of a quasi-self-segment-dense subset. In the absence of demanding technical assumptions, we present new conditions to obtain results on the existence of solutions of nonconvex equilibrium problems in real topological vector spaces via a KKM theorem. Furthermore, no coercivity conditions are used to deal with the noncompact case in reflexive Banach spaces. Examples are provided to compare the obtained results with the literature in convex and nonconvex cases.