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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-05-07983-9
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
MR Author ID: 189912
Email: sreich@tx.technion.ac.il

Stephen Simons
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080
MR Author ID: 189831
Email: simons@math.ucsb.edu

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.