The Convergent Behavior for Parametric Generalized Vector Equilibrium Problems

Abstract

We study some properties for parametric generalized vector equilibrium problems and the convergent behavior for the correspondent solution sets of this problem under some suitable conditions. Several existence results and the topological structures of the efficient solutions set are established. Some new results of existence for weak solutions and strong solutions are derived. Finally, we give some examples to illustrate our theory including the example studied by Fang (1992), who established the perturbed nonlinear program $(P_{\mu })$ and described successfully that the optimal solution of $(P_{\mu })$ will approach the optimal solution of linear program (P).