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Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings

Author: Heinz H. Bauschke
Journal: Proc. Amer. Math. Soc. 135 (2007), 135-139
MSC (2000): Primary 46C05, 47H09; Secondary 52A41, 90C25
Published electronically: August 16, 2006
MathSciNet review: 2280182
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range.

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Additional Information

Heinz H. Bauschke
Affiliation: Department of Mathematics, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, British Columbia, Canada V1V 1V7

Keywords: Fenchel duality, firmly nonexpansive mapping, Fitzpatrick function, Kirszbraun-Valentine theorem
Received by editor(s): July 24, 2005
Published electronically: August 16, 2006
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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