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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem


Authors: Simeon Reich and Stephen Simons
Journal: Proc. Amer. Math. Soc. 133 (2005), 2657-2660
MSC (2000): Primary 46C05, 47H09; Secondary 46N10
Published electronically: March 22, 2005
MathSciNet review: 2146211
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Abstract: We present a new proof of the classical Kirszbraun-Valentine extension theorem. Our proof is based on the Fenchel duality theorem from convex analysis and an analog for nonexpansive mappings of the Fitzpatrick function from monotone operator theory.


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Additional Information

Simeon Reich
Affiliation: Department of Mathematics, The Technion - Israel Institute of Technology, 32000 Haifa, Israel
Email: sreich@tx.technion.ac.il

Stephen Simons
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080
Email: simons@math.ucsb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07983-9
PII: S 0002-9939(05)07983-9
Received by editor(s): April 21, 2004
Published electronically: March 22, 2005
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.