Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 509-521
doi:10.1155/JIA.2005.509
Continuity properties of projection operators
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.
Abstract
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.