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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 6 scientific papers (total in 6 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 (6)
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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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  • https://doi.org/10.4213/tm4229
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    • This publication is cited in the following 6 articles:
    1. E. R. Avakov, G. G. Magaril-Il'yaev, “Controllability of an approximately defined control system”, Sb. Math., 215:4 (2024), 438–463  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. E. R. Avakov, G. G. Magaril-Il'yaev, “Schauder's fixed point theorem and Pontryagin maximum principle”, Izv. Math., 88:6 (2024), 1013–1031  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    3. A. A. Vasileva, A. V. Gorshkov, M. P. Zapletin, L. V. Lokutsievskii, G. G. Magaril-Ilyaev, K. Yu. Osipenko, K. S. Ryutin, A. V. Fursikov, “Ob osnovnykh nauchnykh rezultatakh poslednego vremeni sotrudnikov kafedry obschikh problem upravleniya”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 64–71  mathnet  crossref  elib
    4. A. A. Vasil'eva, A. V. Gorshkov, M. P. Zapletin, L. V. Lokutsievskiy, G. G. Magaril-Il'yaev, K. Yu. Osipenko, K. S. Ryutin, A. V. Fursikov, “Main recent research results of the staff of the Chair of General Problems of Control”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 79:6 (2024), 351–359  mathnet  mathnet  crossref  crossref
    5. E. R. Avakov, G. G. Magaril-Il'yaev, “On the Continuous Dependence of a Solution of a Differential Equation on the Right-Hand Side and Boundary Conditions”, Math. Notes, 114:1 (2023), 3–14  mathnet  crossref  crossref  mathscinet
    6. A. V. Arutyunov, Z. T. Zhukovskaya, S. E. Zhukovskiy, “On the existence of admissible positional controls for systems with mixed constraints”, 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (Moscow, Russian Federation, 2022), 2022, 1–3  crossref
    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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