An inverse mapping theorem in Fréchet-Montel spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00522962" target="_blank" >RIV/67985840:_____/20:00522962 - isvavai.cz</a>
Alternative codes found
RIV/49777513:23520/20:43959195
Result on the web
<a href="https://doi.org/10.1007/s11228-020-00536-2" target="_blank" >https://doi.org/10.1007/s11228-020-00536-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11228-020-00536-2" target="_blank" >10.1007/s11228-020-00536-2</a>
Alternative languages
Result language
angličtina
Original language name
An inverse mapping theorem in Fréchet-Montel spaces
Original language description
Influenced by a recent note by M. Ivanov and N. Zlateva, we prove a statement in the style of Nash-Moser-Ekeland theorem for mappings from a Fréchet-Montel space with values in any Fréchet space (not necessarily standard). The mapping under consideration is supposed to be continuous and directionally differentiable (in particular Gateaux differentiable) with the derivative having a right inverse. We also consider an approximation by a graphical derivative and by a linear operator in the spirit of Graves’ theorem. Finally, we derive corollaries of the abstract results in finite dimensions. We obtain, in particular, sufficient conditions for the directional semiregularity of a mapping defined on a (locally) convex compact set in directions from a locally conic set, and also conditions guaranteeing that the nonlinear image of a convex set contains a prescribed ordered interval.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Set-Valued and Variational Analysis
ISSN
1877-0533
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
14
Pages from-to
195-208
UT code for WoS article
000516224700001
EID of the result in the Scopus database
2-s2.0-85079764691