Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings
Authors:
Heinz H. Bauschke
Affiliation:
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.