Characterizations On Approximate Strictly Efficient Solutions Of Equilibrium Problems

The nonlinear scalarization problem for approximate strictly efficient solutions of vector optimization is considered in locally convex topological spaces.Properties for approximate cones and their interiors are discussed,by applying the nonlinear scalarization functions proposed by G?pfert et al,sufficient and necessary optimality conditions are established for approximate strictly efficient solutions of vector optimization,respectively,and an example is given to illustrate the main result.We consider approximate strictly efficient solutions of the set-valued vector equilibrium problems with constraints and without constraints in locally convex Hausdorff linear topological spaces,present the relationship between the strictly efficient solution and approximate strictly efficient solution.Under the assumption of the near cone-subconvexlikeness,by using separation theorem for convex sets,we obtain Kuhn-Tucker and Lagrange optimality conditions for set-valued vector equilibrium problems with constraints respectively.