Ekeland's principle for set-valued vector equilibrium problems

Abstract

In this paper, we introduce a concept of quasi C-lower semicontinuity for set-valued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ɛ-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.