Abstract and Applied Analysis
Volume 3 (1998), Issue 1-2, Pages 85-103
doi:10.1155/S1085337598000451

Characterizations of metric projections in Banach spaces and applications

Abstract

This paper is devoted to the study of the metric projection onto a nonempty closed convex subset of a general Banach space. Thanks to a systematic use of semi-inner products and duality mappings, characterizations of the metric projection are given. Applications to decompositions of Banach spaces along convex cones and variational inequalities are presented.