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Sbornik: Mathematics, 2022, Volume 213, Issue 1, Pages 1–41
DOI: https://doi.org/10.1070/SM9483 (Mi sm9483) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Global and semilocal theorems on implicit and inverse functions in Banach spaces

A. V. Arutyunov, S. E. Zhukovskiy

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
English version PDF (737 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM9483
Abstract: We consider continuous mappings between two Banach spaces that depend on a parameter with values in a topological space. These mappings are assumed to be continuously differentiable for each value of the parameter. Under normality (regularity) assumptions of the mappings under consideration, we obtain sufficient conditions for the existence of global and semilocal implicit functions. A priori estimates for solutions are given. As an application of these results, we obtain, in particular, a theorem on extending an implicit function from a given closed set to the whole parameter space and a theorem on coincidence points of mappings.
Bibliography: 32 titles.
Keywords: global implicit function, semilocal implicit function, global inversion function theorem, normality condition, continuous extension of an implicit function.
Funding agency Grant number
Russian Science Foundation 20-11-20131
22-21-00863
The results in §§ 5–7 were obtained by A. V. Arutyunov with the support of the Russian Science Foundation (project no. 22-21-00863). The results in §§ 1–4 were obtained by S. E. Zhukovskiy with the support of the Russian Science Foundation (project no. 20-11-20131).
Received: 23.07.2020 and 21.02.2021
Russian version:
Matematicheskii Sbornik, 2022, Volume 213, Number 1, Pages 3–45
DOI: https://doi.org/10.4213/sm9483
Bibliographic databases:
Document Type: Article
UDC: 517.275
MSC: 47J07, 54H25, 26B10
Language: English
Original paper language: Russian
Citation: A. V. Arutyunov, S. E. Zhukovskiy, “Global and semilocal theorems on implicit and inverse functions in Banach spaces”, Mat. Sb., 213:1 (2022), 3–45; Sb. Math., 213:1 (2022), 1–41
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
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