Optimality Conditions For Vector Equilibrium Problems And Well-posedness For Parametric Weak Vector Equilibrium Problems

In this paper, first of all, by using the concepts of various kinds of contingent epiderivatives, we study the optimality conditions for set-valued vector equilibrium problems with functional constraints, and we obtain the necessary and sufficient conditions for the weakly efficient solution and different kinds of properly efficient solutions. Besides, we investigate the parametric uniquely well-posedness and parametric well-posedness for weak vector equilibrium problem in real Banach spaces, establish some metric characterizations of parametric uniquely well-posedness and parametric well-posedness for the problems, and derive some necessary and sufficient conditions of these two kinds of well-posedness.