NECESSARY EFFICIENCY CONDITIONS FOR THE LOCAL HENIG EFFICIENT SOLUTIONS OF V ECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS IN TERMS OF S TUDNIARSKI’S DERIVATIVES

Abstract

The equilibrium problem was first proposed in 1994 by Blum - Oettli which including a number of important problems such as vector variational inequalities, vector optimization problems, fixed poin problems, vector complementarity problems, vector Nash equilibrium problems. Currently, optimality conditions for vector equilibrium problems and vector variational inequalities are widely studied by many authors. In this paper, we’re using the concept of Studniaski’s derivative was proposed by Studniaski in the reference (M. Studniaski (1986)), we establish in this article the necessary efficiency conditions for local Henig efficient solution of vector equilibrium problems with set and generalized inequality constraints in terms of studniarski’s derivatives in Banach spaces. This obtained result is directly applied to local superefficient solution of the problem.