Ekeland's principle for vector equilibrium problem

In this paper, the authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones. The aim is to provide a vector version of Ekeland’s theorem related to equilibrium problems. To prove this principle, a weak notion of continuity of a vectorvalued function is considered, and some of its properties are presented. Via the vector Ekeland’s principle, existence results for vector equilibria are proved in both compact and noncompact domains.