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

By Simeon Reich, Stephen Simons. 2005

102 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/35255d4a7090adcc3599f7b7668c45bba52015f0

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative (2007, unknown): “E-mail: shawn.wang@ubc.ca.”
Some problems about the representation of monotone operators by convex functions (2005, methodology): “For what concerns the sum, we need to use a partial convolution for functions on a product space, as in [ 16] and [20].”