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General Implicit Function Theorem for Close Mappings

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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.

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Authors and Affiliations

  1. V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997, Russia

    E. R. Avakov

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia

    G. G. Magaril-Il’yaev

  3. Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051, Russia

    G. G. Magaril-Il’yaev

  4. Southern Mathematical Institute, Vladikavkaz Scientific Center of Russian Academy of Sciences, ul. Vatutina 53, Vladikavkaz, 362027, Russia

    G. G. Magaril-Il’yaev

Authors
  1. E. R. Avakov
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  2. G. G. Magaril-Il’yaev
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Corresponding author

Correspondence to E. R. Avakov.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 315, pp. 7–18 https://doi.org/10.4213/tm4229.

Translated by I. Nikitin

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Avakov, E.R., Magaril-Il’yaev, G.G. General Implicit Function Theorem for Close Mappings. Proc. Steklov Inst. Math. 315, 1–12 (2021). https://doi.org/10.1134/S0081543821050011

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  • DOI: https://doi.org/10.1134/S0081543821050011

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