On ranges of set-valued mappings
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43965166" target="_blank" >RIV/49777513:23520/22:43965166 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1016/j.jmaa.2022.126381" target="_blank" >https://doi.org/10.1016/j.jmaa.2022.126381</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126381" target="_blank" >10.1016/j.jmaa.2022.126381</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On ranges of set-valued mappings
Popis výsledku v původním jazyce
We derive conditions ensuring that the range of a set-valued 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 convex fbers. Subsequently, in Banach and finite-dimensional spaces, we focus on approximations determined by a convex set of bounded linear mappings such as Páles-Zeidan Jacobian, Clarke's generalized Jacobian, shields by T.H. Sweetser, or Neumaier's interval extensions of the derivative of a smooth mapping. As easy corollaries in Euclidean spaces, we obtain perturbation stability of the property of metric semiregularity under the additive perturbation by a single-valued mapping having sufficiently small calmness modulus; as well as the non-smooth Lyusternik-Graves theorem and Robinson's theorem by A.F. Izmailov. Finally, given two quadratic mappings f and g, a polyhedral convex set O, and an ordered interval K, we provide conditions guaranteeing that an ordered interval L is such that for each y in L there is an x in O with y = f(x) and g(x) in K. This theorem has direct applications in power network security management such as preventing the electricity blackout.
Název v anglickém jazyce
On ranges of set-valued mappings
Popis výsledku anglicky
We derive conditions ensuring that the range of a set-valued 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 convex fbers. Subsequently, in Banach and finite-dimensional spaces, we focus on approximations determined by a convex set of bounded linear mappings such as Páles-Zeidan Jacobian, Clarke's generalized Jacobian, shields by T.H. Sweetser, or Neumaier's interval extensions of the derivative of a smooth mapping. As easy corollaries in Euclidean spaces, we obtain perturbation stability of the property of metric semiregularity under the additive perturbation by a single-valued mapping having sufficiently small calmness modulus; as well as the non-smooth Lyusternik-Graves theorem and Robinson's theorem by A.F. Izmailov. Finally, given two quadratic mappings f and g, a polyhedral convex set O, and an ordered interval K, we provide conditions guaranteeing that an ordered interval L is such that for each y in L there is an x in O with y = f(x) and g(x) in K. This theorem has direct applications in power network security management such as preventing the electricity blackout.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
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)
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
1096-0813
Svazek periodika
515
Číslo periodika v rámci svazku
1
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
19
Strana od-do
1-19
Kód UT WoS článku
000833523600019
EID výsledku v databázi Scopus
2-s2.0-85131444484