Super Efficient Solutions For The Vector Equilibrium Problems

In this paper, it introduces the concept of strong efficient solutions for vector equilibrium and discusses the equivalent results of super efficiency, strong efficiency and Henig efficiency in a locally convex space partially ordered by a convex cone with a bounded base. Under proper conditions it also discusses that the set of super efficient solutions is dense in the set of the efficient solutions for vector equilibrium in locally convex topological vector space. Finally, the paper introduces the concepts of strong superefficiency, weak superefficiency and homogeneous superefficiency and discusses the dual forms of all the kinds of C-superefficiencies for vector equilibrium in locally convex space. The equivalence of all kinds of superefficiencies in the normed space was studied, and their dual forms for vector equilibrium in the normed space with a normal cone were discussed. As an application, the dual forms of various superefficient points are given for vector optimization problems.