Connectedness in vector equilibrium problems involving cones with possibly empty interior

摘要

Sufficient conditions are given, without using scalarizing approaches, for the connectedness of the set of efficient solutions of a vector equilibrium problem in a normed space under the assumption that the ordering cone C has a possibly empty interior and the objective multifunction F is cone-quasiconvex. The above assumptions on C and F exclude all the earlier results that assume that C has a nonempty interior and a base, and F is strongly monotone and cone-convex. (C) 2016 Elsevier B.V. All rights reserved.