On ranges of non-linear operators

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43965164" target="_blank" >RIV/49777513:23520/22:43965164 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11228-021-00619-8" target="_blank" >https://doi.org/10.1007/s11228-021-00619-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11228-021-00619-8" target="_blank" >10.1007/s11228-021-00619-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On ranges of non-linear operators

Popis výsledku v původním jazyce

We derive conditions ensuring that the range of a given continuous mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued mapping such that the inverse of it has either convex fibers or admits a continuous single-valued selection. Subsequently, in Banach and finite-dimensional spaces, we focus on approximations determined by a convex set of bounded linear mappings. We demonstrate that our approach is highly flexible and provides the unified treatment of various, in general non-local, covering properties of possibly non-smooth mappings. In finite-dimensional spaces, we present sufficient conditions for constrained directional semiregularity, metric regularity and strong metric regularity. These conditions cover, unify, and extend such well-known results as Pourciau’s open mapping theorem and Clarke’s inverse and implicit function theorems as well as their generalizations established by V. Jeyakumar and D.T. Luc by using upper semi-continuous unbounded pseudo-Jacobians or by A. Neumaier by considering various interval extensions of the derivative of a smooth mapping. Finally, we provide conditions guaranteeing that the non-linear image of a compact convex set contains a prescribed ordered interval which has direct applications in power network security management such as preventing the electricity blackout.

Název v anglickém jazyce

On ranges of non-linear operators

Popis výsledku anglicky

We derive conditions ensuring that the range of a given continuous mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued mapping such that the inverse of it has either convex fibers or admits a continuous single-valued selection. Subsequently, in Banach and finite-dimensional spaces, we focus on approximations determined by a convex set of bounded linear mappings. We demonstrate that our approach is highly flexible and provides the unified treatment of various, in general non-local, covering properties of possibly non-smooth mappings. In finite-dimensional spaces, we present sufficient conditions for constrained directional semiregularity, metric regularity and strong metric regularity. These conditions cover, unify, and extend such well-known results as Pourciau’s open mapping theorem and Clarke’s inverse and implicit function theorems as well as their generalizations established by V. Jeyakumar and D.T. Luc by using upper semi-continuous unbounded pseudo-Jacobians or by A. Neumaier by considering various interval extensions of the derivative of a smooth mapping. Finally, we provide conditions guaranteeing that the non-linear image of a compact convex set contains a prescribed ordered interval which has direct applications in power network security management such as preventing the electricity blackout.

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

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Set-Valued and Variational Analysis: theory and applications

ISSN

1877-0533

e-ISSN

1877-0541

Svazek periodika

30

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

789-810

Kód UT WoS článku

000750324900001

EID výsledku v databázi Scopus

2-s2.0-85123931182