Asplund sets, differentiability and subdifferentiability of functions in Banach spaces
type: Item
instance of: scholarly article
title: Asplund sets, differentiability and subdifferentiability of functions in Banach spaces
zbMATH Open document ID: 1122.46022
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-12-07T00:00:00Z
review text: Preiss' celebrated differentiability theorem and the Borwein--Preiss variational principle apply (in the Fréchet case) to functions which are defined on Asplund spaces. The purpose of the present work is to investigate differentiability of functions defined on general Banach spaces, but along directions which belong to a given Asplund set \(M\). It is shown that Stegall's factorization theorem allows indeed to carry over the classical results to this frame, and for instance to extend a result of Giles and Sciffer by showing that Lipschitz functions are densely \(M\)-differentiable when \(M\) is an Asplund set, and a result of Fabian by showing dense \(M\)-subdifferentiability of lower semi-continuous functions.
reviewed by: Gilles Godefroy
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 46T20
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 49J50
zbMATH DE Number: 5077918
zbMATH Keywords: Asplund set
zbMATH Keywords: M-differentiability and subdifferentiability
zbMATH Keywords: Asplund generated space
author: Xianfu Wang
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.11.074
OpenAlex ID: W2000016087
cites work: Partially smooth variational principles and applications
cites work: A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
cites work: Null Sets and Essentially Smooth Lipschitz Functions
cites work: Geometric aspects of convex sets with the Radon-Nikodym property
cites work: Q4000274
cites work: Theorems of Namioka and R. E. Johnson Type for Upper Semicontinuous and Compact Valued Set-Valued Mappings
cites work: Subdifferential calculus in Asplund generated spaces
cites work: Q3200121
cites work: Q4339230
cites work: On Intermediate Differentiability of Lipschitz Functions on Certain Banach Spaces
cites work: Fréchet differentiability of regular locally Lipschitzian functions
cites work: Frechet vs. Gateaux Differentiability of Lipschitzian Functions
cites work: Q4801806
cites work: A characterisation of minimal subdifferential mappings of locally Lipschitz functions
cites work: Nonsmooth sequential analysis in Asplund spaces
cites work: Convex functions, monotone operators and differentiability.
cites work: Differentiability of Lipschitz functions on Banach spaces
cites work: The Radon-Nikodym Property in Conjugate Banach Spaces. II
DOI: 10.1016/J.JMAA.2005.11.074
description: scientific article; zbMATH DE number 5077918