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

Bauschke, Heinz

doi:10.1090/S0002-9939-06-08770-3

Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings
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by Heinz H. Bauschke PDF

Proc. Amer. Math. Soc. 135 (2007), 135-139 Request permission

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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