Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Fechner, Włodzimierz

Journal of Applied Analysis

Editor-in-Chief: Liczberski, Piotr / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw


CiteScore 2017: 0.33

SCImago Journal Rank (SJR) 2017: 0.183
Source Normalized Impact per Paper (SNIP) 2017: 0.364

Mathematical Citation Quotient (MCQ) 2017: 0.27

Online
ISSN
1869-6082
See all formats and pricing
More options …
Volume 18, Issue 2

Issues

Extending Lipschitz mappings continuously

Eva Kopecká
  • Mathematical Institute, Czech Academy of Sciences, Žitná 25, 11567 Prague, Czech Republic; and Institut für Analysis, Johannes Kepler Universität, 4040 Linz, Austria
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2012-11-27 | DOI: https://doi.org/10.1515/jaa-2012-0011

Abstract.

We consider short mappings from a bounded subset of a Euclidean space into that space, that is, mappings which do not increase distances between points. By Kirszbraun's theorem any such mapping can be extended to the entire space to be short again. In general, the extension is not unique. We show that there are single-valued extension operators continuous in the supremum norm. The multivalued extension operator is lower semicontinuous.

Keywords: Lipschitz mapping; extension; Hilbert space

About the article

Received: 2011-05-17

Revised: 2011-05-27

Accepted: 2011-06-10

Published Online: 2012-11-27

Published in Print: 2012-12-01


Citation Information: , Volume 18, Issue 2, Pages 167–177, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/jaa-2012-0011.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Rafa Espínola and Adriana Nicolae
Revista Matemática Complutense, 2015, Volume 28, Number 3, Page 741

Comments (0)

Please log in or register to comment.
Log in