An inverse mapping theorem in Fréchet-Montel spaces

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/49777513:23520/20:43959195

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

An inverse mapping theorem in Fréchet-Montel spaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

An inverse mapping theorem in Fréchet-Montel spaces

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Set-Valued and Variational Analysis

ISSN

1877-0533

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

195-208

Kód UT WoS článku

000516224700001

EID výsledku v databázi Scopus

2-s2.0-85079764691