On Stegall's smooth variational principle
type: Item
instance of: scholarly article
title: On Stegall's smooth variational principle
zbMATH Open document ID: 1117.46014
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-01-11T00:00:00Z
review text: A well-known perturbation of the result in the title is that if a Banach space has the Radon--Nikodým Property, then any coercive lower semicontinuous bounded below function defined on it admits an arbitrarily small linear variation which attains a strong minimum. The authors note that the converse is also true. More significantly, they prove that either of the following formally weaker conditions is also equivalent to the Radon--Nikodým Property: (i) any coercive continuous bounded below function defined on the space admits a linear variation which attains a minimum, (ii) any coercive continuous convex bounded below function defined on the space admits a linear variation which attains a strong minimum. One may note that the obvious common weakening of these two conditions is not interesting, as it holds for every Banach space.
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46N10
zbMATH DE Number: 5115282
zbMATH Keywords: variational principle
zbMATH Keywords: Radon-Nikodým Property
author: Marián Fabian
author: C. Finet
MaRDI profile type: Publication
full work available at URL: j.na.2005.11.047
OpenAlex ID: W1992771789
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DOI: 10.1016/J.NA.2005.11.047
description: scientific article; zbMATH DE number 5115282