Frechet differentiability via partial Frechet differentiability
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475585" target="_blank" >RIV/00216208:11320/23:10475585 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rg~m4_.I9d" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rg~m4_.I9d</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2023.025" target="_blank" >10.14712/1213-7243.2023.025</a>
Alternative languages
Result language
angličtina
Original language name
Frechet differentiability via partial Frechet differentiability
Original language description
Let X-1 , ... , X-n be Banach spaces and f a real function on X = X-1 x <middle dot> <middle dot> <middle dot> x X-n. Let A(f) be the set of all points x is an element of X at which f is partially Frechet differentiable but is not Frechet differentiable. Our results imply that if X-1 , ... , Xn-1 are Asplund spaces and f is continuous (respectively Lipschitz) on X, then A(f) is a first category set (respectively a sigma-upper porous set). We also prove that if X, Y are separable Banach spaces and f : X -> Y is a Lipschitz mapping, then there exists a sigma-upper porous set A subset of X such that f is Frechet differentiable at every point x is an element of X A at which it is Frechet differentiable along a closed subspace of finite codimension and G & aacute;teaux differentiable. A number of related more general results are also proved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Commentationes Mathematicae Universitatis Carolinae
ISSN
0010-2628
e-ISSN
1213-7243
Volume of the periodical
64
Issue of the periodical within the volume
2
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
23
Pages from-to
185-207
UT code for WoS article
001100839300004
EID of the result in the Scopus database
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