Efficiencies and Pareto efficiencies of set-valued mappings on ordered spaces

摘要

In this paper, we extend the concepts of the maximal and minimal efficiencies of nonempty subsets with respect to a convex cones in topological vector spaces to maximum, minimum, maximal and minimal efficiencies of set-valued mappings on general ordered spaces. Some properties and examples are provided. We prove some existence theorems on ordered topological vector spaces which are applied to solve some generalized vector variational inequalities for set- valued mappings.