Lipschitz behaviour of the Legendre-Fenchel transform
type: Item
instance of: scholarly article
title: Lipschitz behaviour of the Legendre-Fenchel transform
zbMATH Open document ID: 0824.90108
DOI: 10.1007/BF01027091
author: A. Rahmouni
author: D. Azé
published in: Set-Valued Analysis
publication date: 1994-08-31T00:00:00Z
review text: An estimate of the modulus of continuity of the Legendre-Fenchel transform, acting on the set of extended real-valued convex functions, is given. The functions are defined on a normed vector space or on its dual space equipped with the Attouch-Wets topology. It is proved further that the Legendre-Fenchel transform has a locally Lipschitz behaviour when the set of closed proper convex functions is endowed with suitable families of semimetrics.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 627462
zbMATH Keywords: normed vector space
zbMATH Keywords: Attouch-Wets topology
zbMATH Keywords: Legendre-Fenchel transform
reviewed by: Karel Zimmermann
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01027091
OpenAlex ID: W2072691731
description: scientific article; zbMATH DE number 627462