On ranges of non-linear operators

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

On ranges of non-linear operators

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure 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

Name of the periodical

Set-Valued and Variational Analysis: theory and applications

ISSN

1877-0533

e-ISSN

1877-0541

Volume of the periodical

30

Issue of the periodical within the volume

2

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

22

Pages from-to

789-810

UT code for WoS article

000750324900001

EID of the result in the Scopus database

2-s2.0-85123931182