Abstract and Applied Analysis
Volume 3 (1998), Issue 1-2, Pages 85-103

Characterizations of metric projections in Banach spaces and applications

Jean-Paul Penot and Robert Ratsimahalo

Laboratoire de Mathématiques Appliquées UPRES-A 5033 CNRS, Université de Pau et des Pays de l'Adour, Av. de l'Université, Pau 64000, France

Received 15 May 1997

Copyright © 1998 Jean-Paul Penot and Robert Ratsimahalo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.