Open Access

Continuity properties of projection operators

Journal of Inequalities and Applications20052005:921970

DOI: 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 https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.509/MediaObjects/13660_2003_Article_1561_IEq1_HTML.gif 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 https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.509/MediaObjects/13660_2003_Article_1561_IEq2_HTML.gif of a given point when https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.509/MediaObjects/13660_2003_Article_1561_IEq3_HTML.gif varies.

Authors’ Affiliations

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

Copyright

© Penot 2005