Skip to main content
Journal of Inequalities and Applications
Download PDF
  • Research Article
  • Open access
  • Published:

Continuity properties of projection operators

Journal of Inequalities and Applications volume 2005, Article number: 921970 (2005) Cite this article

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.

Author information

Authors and Affiliations

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

    Jean-Paul Penot

Authors
  1. Jean-Paul Penot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jean-Paul Penot.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Penot, JP. Continuity properties of projection operators. J Inequal Appl 2005, 921970 (2005). https://doi.org/10.1155/JIA.2005.509

Download citation

  • Received:

  • Published:

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