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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F14%3A10285323%21RIV15-MSM-11320___
rdf:type
n4:Vysledek skos:Concept
dcterms:description
Let X be a separable Banach space, Y a Banach space and f : X -> Y an arbitrary mapping. Then the following implication holds at each point x is an element of X except a sigma-directionally porous set: If the one-sided Hadamard directional derivative f(H+)'(x,u) exists in all directions u from a set S-x subset of X whose linear span is dense in X, then f is Hadamard differentiable at x. This theorem improves and generalizes a recent result of A. D. Ioffe, in which the linear span of S-x equals X and Y = R. An analogous theorem, in which f is pointwise Lipschitz, and which deals with the usual one-sided derivatives and Gateaux differentiability is also proved. It generalizes a result of D. Preiss and the author, in which f is supposed to be Lipschitz. Let X be a separable Banach space, Y a Banach space and f : X -> Y an arbitrary mapping. Then the following implication holds at each point x is an element of X except a sigma-directionally porous set: If the one-sided Hadamard directional derivative f(H+)'(x,u) exists in all directions u from a set S-x subset of X whose linear span is dense in X, then f is Hadamard differentiable at x. This theorem improves and generalizes a recent result of A. D. Ioffe, in which the linear span of S-x equals X and Y = R. An analogous theorem, in which f is pointwise Lipschitz, and which deals with the usual one-sided derivatives and Gateaux differentiability is also proved. It generalizes a result of D. Preiss and the author, in which f is supposed to be Lipschitz.
dcterms:title
Gateaux and Hadamard Differentiability via Directional Differentiability Gateaux and Hadamard Differentiability via Directional Differentiability
skos:prefLabel
Gateaux and Hadamard Differentiability via Directional Differentiability Gateaux and Hadamard Differentiability via Directional Differentiability
skos:notation
RIV/00216208:11320/14:10285323!RIV15-MSM-11320___
n3:aktivita
n7:P n7:I
n3:aktivity
I, P(GAP201/12/0436)
n3:cisloPeriodika
3
n3:dodaniDat
n8:2015
n3:domaciTvurceVysledku
n11:7357362
n3:druhVysledku
n18:J
n3:duvernostUdaju
n17:S
n3:entitaPredkladatele
n13:predkladatel
n3:idSjednocenehoVysledku
17957
n3:idVysledku
RIV/00216208:11320/14:10285323
n3:jazykVysledku
n9:eng
n3:klicovaSlova
pointwise Lipschitz mapping; sigma-directionally porous set; Hadamard directional derivatives; directional derivatives; Hadamard differentiability; Gateaux differentiability
n3:klicoveSlovo
n5:directional%20derivatives n5:Hadamard%20differentiability n5:Hadamard%20directional%20derivatives n5:Gateaux%20differentiability n5:sigma-directionally%20porous%20set n5:pointwise%20Lipschitz%20mapping
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[A65D7B9D8525]
n3:nazevZdroje
Journal of Convex Analysis
n3:obor
n15:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n16:GAP201%2F12%2F0436
n3:rokUplatneniVysledku
n8:2014
n3:svazekPeriodika
21
n3:tvurceVysledku
Zajíček, Luděk
n3:wos
000342730400006
s:issn
0944-6532
s:numberOfPages
11
n14:organizacniJednotka
11320