VARIATIONAL INEQUALITIES AND COMPLEMENTARITY PROBLEM FOR PM-MAPS

Abstract

Let X be a reflexive Banach space and X* its dual space. Applying the property of pseudo-monotone map and maximal monotonicity of subdifferential, we discuss the existence of solutions of the variational inequalities and complementarity problem for PM-map in X. When both X and X* are uniformly convex Banach spaces, We give the necessary and suffcient condition that the map T having nearest point in J(D), and study the equivalent conditions to J-T having zero point in D.