Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings
Heinz H. Bauschke · Proceedings of the American Mathematical Society · 2006
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.