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Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings |
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| Authors: | Heinz H Bauschke |
| Institution: | Department of Mathematics, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, British Columbia, Canada V1V 1V7 |
| 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. |
| Keywords: | Fenchel duality firmly nonexpansive mapping Fitzpatrick function Kirszbraun-Valentine theorem |
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