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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 315, Pages 7–18
DOI: https://doi.org/10.4213/tm4229 (Mi tm4229) 		 
This article is cited in 3 scientific papers (total in 3 papers)

General Implicit Function Theorem for Close Mappings

E. R. Avakova, G. G. Magaril-Il'yaevbcd

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
Full-text PDF (218 kB) Citations (3)
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DOI: https://doi.org/10.4213/tm4229
Abstract: We prove a sufficiently general implicit function theorem for mappings that are close to an original one in the uniform metric of the space of continuous mappings. As a corollary, we derive an important (for applications) result related to perturbations of linear mappings.
Keywords: implicit function, close mappings, metric regularity.
Received: February 24, 2021
Revised: April 29, 2021
Accepted: July 12, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 315, Pages 1–12
DOI: https://doi.org/10.1134/S0081543821050011
Bibliographic databases:
Document Type: Article
UDC: 517.51+517.97
Language: Russian
Citation: E. R. Avakov, G. G. Magaril-Il'yaev, “General Implicit Function Theorem for Close Mappings”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 7–18; Proc. Steklov Inst. Math., 315 (2021), 1–12
Citation in format AMSBIB
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\paper General Implicit Function Theorem for Close Mappings
\inbook Optimal Control and Differential Games
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 315
\pages 7--18
\publ Steklov Math. Inst.
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4229}
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\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 315
\pages 1--12
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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