On ranges of set-valued mappings

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On ranges of set-valued mappings
Original language description
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.
Czech name
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Czech description
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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
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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