On the Metric Projection Operator and Its Applications to Solving Variational Inequalities in Banach Spaces

Abstract

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.