Gâteaux and Hadamard differentiability via directional differentiability
type: Item
instance of: scholarly article
zbMATH Open document ID: 1311.46044
publication date: 2014-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1211.2604
full work available at URL: jca21037.htm
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 49J50
zbMATH DE Number: 6353706
zbMATH Keywords: Hadamard derivative
zbMATH Keywords: Gâteaux derivative
zbMATH Keywords: directional derivative
zbMATH Keywords: \(\sigma\)-directionally porous set
zbMATH Keywords: pointwise Lipschitz mapping
author: Luděk Zajíček
MaRDI profile type: Publication
arXiv ID: 1211.2604
arXiv classification: math.FA
title: Gâteaux and Hadamard differentiability via directional differentiability
published in: Journal of Convex Analysis
review text: The author inspects the Gâteaux and Hadamard differentiablity as implied by directional differentiablity. The Ioffe result on the Hadamard differentiability is improved and generalized for vector-valued functions; cf. [\textit{A. Ioffe}, J. Convex Anal. 17, No. 3--4, 1019--1032 (2010; Zbl 1208.46043)].NEWLINENEWLINEAn analogous result on the connection between directional and Gâteaux derivatives is established, which generalizes a previous joint result by \textit{D. Preiss} and the author; see [Isr. J. Math. 125, 1--27 (2001; Zbl 1022.46026)].
reviewed by: S. S. Kutateladze
description: scientific article; zbMATH DE number 6353706