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

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

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.