Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 509-521

Continuity properties of projection operators

Jean-Paul Penot

Laboratoire de Mathématiques Appliquées, CNRS FRE 2570, Faculté des Sciences, Universit'e de Pau, Avenue de l'Université, Pau 64000, France

Received 31 December 2003

Copyright © 2005 Jean-Paul Penot. 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.


We prove that the projection operator on a nonempty closed convex subset C of a uniformly convex Banach spaces is uniformly continuous on bounded sets and we provide an estimate of its modulus of uniform continuity. We derive this result from a study of the dependence of the projection on C of a given point when C varies.