A generalized Ekeland’s variational principle for vector equilibria - MIHOLCA, Mihaela (Studia Universitatis Babeș-Bolyai Mathematica, 2019)
In this paper, we establish an Ekeland-type variational principle for vector valued bifunctions defined on complete metric spaces with values in locally convex spaces ordered by closed convex cones. The main improvement consists in widening the class of bifunctions for which the variational principle holds. In order to prove this principle, a weak notion of continuity for vector valued functions is considered, and some of its properties are presented. We also furnish an existence result for vector equilibria in absence of convexity assumptions, passing through the existence of approximate solutions of an optimization problem. Mathematics Subject Classification (2010): 49J35, 49K40, 49J52.