EXISTENCE OF SOLUTIONS AND WELL-POSEDNESS FOR BILEVEL VECTOR EQUILIBRIUM PROBLEMS

In this paper, we investigate existence of solutions and well-posedness of bilevel vector equilibrium problems. The existence of solution and approximating solution are established by using Fan-KKM theorem. The relations among the uniqueness of solution and the upper semicontinuity or continuity of approximating solution set and the well-posedness of bilevel vector equilibrium problem. We also prove that the generalized well-posedness can be equivalently characterized by the compactness of the solution set and the upper semicontinuity of the approximating solution set. Finally, metric characterizations of the generalized well-posedness are derived in terms of the excess and Kuratowski measure of noncompactness of the approximating solution set under some suitable conditions which ensure the existence of solution of bilevel vector equilibrium problem.