ON THE METRIC PROJECTION OPERATOR AND ITS APPLICATIONS TO SOLVING VARIATIONAL INEQUALITIES IN BANACH SPACES

In this paper, we investigate the characteristics of the metric projection operator P K : B → K, where B is a Banach space with dual space B∗, and K is a nonempty closed convex subset of B. Then we apply its properties to study the existence of solutions of variational inequalities in uniformly convex and uniformly smooth Banach spaces.