HADAMARD DIFFERENTIABILITY VIA GATEAUX DIFFERENTIABILITY
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10316293" target="_blank" >RIV/00216208:11320/15:10316293 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
HADAMARD DIFFERENTIABILITY VIA GATEAUX DIFFERENTIABILITY
Original language description
Let f be a mapping from a separable Banach space to a Banach space. We prove that, except for a sigma-directionally porous set, f is Hadamard differentiable at those points, at which f is Lipschitz and Gateaux differentiable. As a consequence we obtain that an everywhere Gateaux differentiable mapping from an Euclidean space to a Banach space is Frechet differentiable except for a nowhere dense sigma-porous set.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP201%2F12%2F0436" target="_blank" >GAP201/12/0436: Theory of Real Functions and Descriptive Set Theory III</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
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Volume of the periodical
143
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
279-288
UT code for WoS article
000351490000029
EID of the result in the Scopus database
2-s2.0-84924765766