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Matematicheskie Zametki, 2023, Volume 113, Issue 6, Pages 793–806
DOI: https://doi.org/10.4213/mzm13518 (Mi mzm13518) 		 
Implicit Function Theorems for Continuous Mappings and Their Applications

A. V. Arutyunova, S. E. Zhukovskiya, B. Sh. Mordukhovichb

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
b Wayne State University, Detroit, MI, USA
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DOI: https://doi.org/10.4213/mzm13518
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.
Keywords: implicit function, regular coderivative, minimum function.
Funding agency Grant number
Russian Science Foundation 20-11-20131
22-11-00042
A. V. Arutyunov was supported by the Russian Science Foundation under grant no. 20-11-20131. S. E. Zhukovskiy was supported by the Russian Science Foundation under grant no. 22-11-00042.
Received: 30.03.2022
Revised: 11.07.2022
Published: 01.06.2023
English version:
Mathematical Notes, 2023, Volume 113, Issue 6, Pages 749–759
DOI: https://doi.org/10.1134/S0001434623050164
Bibliographic databases:
Document Type: Article
UDC: 517
MSC: 49J52
Language: Russian
Citation: A. V. Arutyunov, S. E. Zhukovskiy, B. Sh. Mordukhovich, “Implicit Function Theorems for Continuous Mappings and Their Applications”, Mat. Zametki, 113:6 (2023), 793–806; Math. Notes, 113:6 (2023), 749–759
Citation in format AMSBIB
\Bibitem{AruZhuMor23}
\by A.~V.~Arutyunov, S.~E.~Zhukovskiy, B.~Sh.~Mordukhovich
\paper Implicit Function Theorems for Continuous Mappings
and Their Applications
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 6
\pages 793--806
\mathnet{http://mi.mathnet.ru/mzm13518}
\crossref{https://doi.org/10.4213/mzm13518}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4602438}
\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 6
\pages 749--759
\crossref{https://doi.org/10.1134/S0001434623050164}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85162134018}
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