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Mat. Zametki, 2012, Volume 91, Issue 6, Pages 813–818 (Mi mz9383)  

This article is cited in 3 scientific papers (total in 3 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

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

DOI: https://doi.org/10.4213/mzm9383

Full text: PDF file (459 kB)
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English version:
Mathematical Notes, 2012, 91:6, 764–769

Bibliographic databases:

UDC: 517.51
Received: 28.09.2010
Revised: 13.01.2011

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
  • http://mi.mathnet.ru/eng/mz/v91/i6/p813

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Arutyunov A., Zhukovskiy S., “Continuous Dependence of Coincidence Points on a Parameter”, Set-Valued Var. Anal., 23:1 (2015), 23–41  crossref  mathscinet  zmath  isi  scopus
    2. R. A. Khachatryan, “Ob odnoi teoreme o neyavnykh funktsiyakh v negladkom sluchae”, Vladikavk. matem. zhurn., 19:4 (2017), 86–96  mathnet
    3. E. R. Avakov, G. G. Magaril-Il'yaev, “An Implicit Function Theorem for Inclusions Defined by Close Mappings”, Math. Notes, 103:4 (2018), 507–512  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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