Existence of equilibria in complete metric spaces

In this paper, we establish equilibrium version of Ekeland's variational principle without assuming any kind of semicontinuity of the bifunction involved in the formulation of the principle. By using such principle, we derive some existence results for a solution of equilibrium problems with or without compactness assumption on the underlying set. A coercivity condition is introduced to obtain a solution of an equilibrium problem for noncompact case. Our results extend and improve several known results in the literature.