Ekeland variational principles for vector equilibrium problems with solid ordering cones

Abstract

This paper concerns with Ekeland variational principles for vector bifunctions. It is assumed that the topological interior of the ordering cone in the final space of the bifunction is nonempty. The main results are stated by nonlinear scalarization through the well-known Gerstewitz functional, and involve a new lower-semicontinuity concept for vector functions and a generalization of the so-called triangle inequality property of a vector bifunction. Some recent Ekeland variational principles of the literature derived for a kind of Henig approximate solutions of vector equilibrium problems are improved as they are obtained by weaker assumptions.