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Matematicheskie Zametki, 2012, Volume 91, Issue 6, Pages 813–818
DOI: https://doi.org/10.4213/mzm9383
(Mi mzm9383)
 

This article is cited in 7 scientific papers (total in 7 papers)

An Implicit-Function Theorem for Inclusions

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

a Institute of Control Sciences, Russian Academy of Sciences, Moscow
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
c South Mathematical Institute of VSC RAS
Full-text PDF (459 kB) Citations (7)
References:
Abstract: We consider the question of the solvability of an inclusion $F(x,\sigma)\in A$, i.e., of determining a mapping (implicit function) $\sigma\mapsto x(\sigma)$ defined on a set such that $F(x(\sigma),\sigma)\in A$ for any $\sigma$ from this set. Results of this kind play a key role in the different branches of analysis and, especially, in the theory of extremal problems, where they are the main tool for deriving conditions for an extremum.
Keywords: implicit-function theorem, nonlinear equation, Newton's method, Banach space, multivalued mapping, continuous selector.
Received: 28.09.2010
Revised: 13.01.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 6, Pages 764–769
DOI: https://doi.org/10.1134/S0001434612050227
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: E. R. Avakov, G. G. Magaril-Il'yaev, “An Implicit-Function Theorem for Inclusions”, Mat. Zametki, 91:6 (2012), 813–818; Math. Notes, 91:6 (2012), 764–769
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm9383
  • https://www.mathnet.ru/eng/mzm/v91/i6/p813
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:44
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