Fenchel duality, Fitzpatrick functions and the Kirszbraun–Valentine extension theorem

Reich, Simeon; Simons, Stephen

doi:10.1090/S0002-9939-05-07983-9

Fenchel duality, Fitzpatrick functions and the Kirszbraun–Valentine extension theorem
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Proc. Amer. Math. Soc. 133 (2005), 2657-2660 Request permission

Abstract:

We present a new proof of the classical Kirszbraun–Valentine extension theorem. Our proof is based on the Fenchel duality theorem from convex analysis and an analog for nonexpansive mappings of the Fitzpatrick function from monotone operator theory.

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