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Approximation of Lipschitz functions by Δ-convex functions in banach spaces

 

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Opened Access Approximation of Lipschitz functions by Δ-convex functions in banach spaces
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Author: Cepedello Boiso, Manuel
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 1998-12
Published in: Israel Journal of Mathematics, 106 (1), 269-284.
Document type: Article
Abstract: In this paper we give some results about the approximation of a Lipschitz function on a Banach space by means of ∆-convex functions. In particular, we prove that the density of ∆-convex functions in the set of Lipschitz functions for the topology of uniform convergence on bounded sets characterizes the superreflexivity of the Banach space. We also show that Lipschitz functions on superreflexive Banach spaces are uniform limits on the whole space of ∆-convex functions.
Cite: Cepedello Boiso, M. (1998). Approximation of lipschitz functions by Δ-convex functions in banach spaces. Israel Journal of Mathematics, 106 (1), 269-284.
Size: 195.0Kb
Format: PDF

URI: http://hdl.handle.net/11441/43521

DOI: 10.1007/BF02773472

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