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

DOI10.1090/S0002-9939-05-07983-9zbMath1075.46020OpenAlexW1501681399MaRDI QIDQ4674765

Stephen Simons, Simeon Reich

Publication date: 18 May 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-07983-9

zbMATH Keywords

nonexpansive mappingHilbert spaceFenchel duality theoremKirszbraun--Valentine extension theorem

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

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Cites Work

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• The range of sums of accretive and monotone operators
• Image d'une somme d'opérateurs monotones et applications
• Extension problems for accretive sets in Banach spaces
• Extension of Fenchel's duality theorem for convex functions
• A new proof for Rockafellar’s characterization of maximal monotone operators
• On the extension of a transformation
• On a Theorem of Kirzbraun and Valentine
• A Lipschitz Condition Preserving Extension for a Vector Function

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