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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

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Volume 18, Issue 2


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
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Published Online: 2012-11-27 | DOI: https://doi.org/10.1515/jaa-2012-0011


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.

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