Variationall Inequalities And Complementary Problem Including PM-map

In this paper, X denotes a reflexive Banach space. We apply acute angle principle and theory of recession operator to discuss the existence of solution of the variational inequalities for PM-map(T) and compieme- ntarity problem in X. And when both X and X* are Banach space of uniform convex, we discuss the sufficient and necessary condition of equivalency about the map T having nearest point in J(D) and J-T having zero point in D.