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

Author: Li Jinlu  

Publisher: Taylor & Francis Ltd

ISSN: 0163-0563

Source: Numerical Functional Analysis and Optimization, Vol.29, Iss.3-4, 2008-03, pp. : 410-418

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Abstract

In this paper, we investigate the characteristics of the metric projection operator PK: 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.