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Implicit Function Theorems for Continuous Mappings and Their Applications

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Abstract

Local and nonlocal implicit function theorems are obtained for closed mappings with a parameter from one Asplund space to another. These theorems are formulated in terms of the regular coderivative of a mapping at a point. The obtained results are applied to study properties of the minimum function for a constrained extremum problem with equality-type constraints and with a parameter. Sufficient conditions for the upper semicontinuity of the minimum function for a given parameter value are obtained.

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Funding

A. V. Arutyunov was supported by the Russian Science Foundation under grant no. 20-11-20131, https://rscf.ru/en/project/20-11-20131/. S. E. Zhukovskiy was supported by the Russian Science Foundation under grant no. 22-11-00042, https://rscf.ru/en/project/22-11-00042/. B. S. Mordukhovich was supported by the US National Science Foundation under grants no. DMS-1808978 and DMS-2204519.

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Authors and Affiliations

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

    A. V. Arutyunov & S. E. Zhukovskiy

  2. Wayne State University, Detroit, MI, 48202, United States of America

    B. Sh. Mordukhovich

Authors
  1. A. V. Arutyunov
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  2. S. E. Zhukovskiy
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  3. B. Sh. Mordukhovich
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Corresponding author

Correspondence to S. E. Zhukovskiy.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 793–806 https://doi.org/10.4213/mzm13518.

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Arutyunov, A.V., Zhukovskiy, S.E. & Mordukhovich, B.S. Implicit Function Theorems for Continuous Mappings and Their Applications. Math Notes 113, 749–759 (2023). https://doi.org/10.1134/S0001434623050164

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