Sensitivity Analysis And Stability For Vector Equilibriums In Banach Space

The differential properties of a class of set-valued maps and gap functions involving vector equilibrium was investigated in the chapter2of this paper, using the concept of contingent derivative.the relationship between the contingent derivatives were discussed.A formula was established to calculate the contingent derivative of the gap function. By applying a presents a new concept of cone convex of bi-function,it obtained of the gap function G and the set-valued map G-C.The sensitivity analysis was studied in infinite dimensional reflexive Banach spaces.By using the concept of P-K convergence of sequences of subsets, we investigate stability of weak efficient solutions for vector equilibrium problems under discrete dilation in the chapter3of this paper. A new concept of approximating sequence of set-valued maps for weak vector equilibrium problem is given out. Various sufficient conditions are provided to ensure the inclusion of the set of solution, and a number of examples are used to illustrate the corresponding results.