Open Access

Continuity properties of projection operators

Journal of Inequalities and Applications20052005:921970

https://doi.org/10.1155/JIA.2005.509

Received: 31 December 2003

Published: 31 October 2005

Abstract

We prove that the projection operator on a nonempty closed convex subset 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 of a given point when varies.

Authors’ Affiliations

(1)
Laboratoire de Mathématiques Appliquées, CNRS FRE 2570, Faculté des Sciences, Universit'e de Pau

Copyright

© Penot 2005