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Russian Universities Reports. Mathematics, 2019, Volume 24, Issue 126, Pages 141–149
DOI: https://doi.org/10.20310/1810-0198-2019-24-126-141-149
(Mi vtamu142)
 

This article is cited in 1 scientific paper (total in 1 paper)

Scientific articles

Existence of inverse function in a neighbourhood of a critical value

S. E. Zhukovskiyab, T. T. Ngoka

a RUDN University
b V. A. Trapeznikov Institute of Control Sciences of RAS
Full-text PDF (436 kB) Citations (1)
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Abstract: The classical inverse function theorems guarantee the existence of an inverse function in a neighborhood of the value of a given point if the regularity condition is satisfied at this point, that is, the first derivative at a given point is nondegenerate. A more general condition for the existence of an implicit function is the 2-regularity condition. It holds, for example, for many quadratic mappings at zero. It is known that under natural smoothness assumptions, the existence of a continuous inverse function follows from a 2-regularity of a map at a point in a certain direction. In this paper, it is shown that, in the known statements guaranteeing the existence of an inverse function when the 2-regularity condition is satisfied, we can weaken the smoothness assumptions. However, the inverse function may not be continuous.
Keywords: inverse function, 2 -regularity.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00080
Russian Science Foundation 17-11-01168
The work is partially supported by the Russian Foundation for Basic Research (project no. 19-01-00080_a). The results of Section 3 are due to the first author who was supported by the Russian Science Foundation (project no. 17-11-01168).
Received: 20.02.2019
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: S. E. Zhukovskiy, T. T. Ngok, “Existence of inverse function in a neighbourhood of a critical value”, Russian Universities Reports. Mathematics, 24:126 (2019), 141–149
Citation in format AMSBIB
\Bibitem{ZhuNgo19}
\by S.~E.~Zhukovskiy, T.~T.~Ngok
\paper Existence of inverse function in a neighbourhood of a critical value
\jour Russian Universities Reports. Mathematics
\yr 2019
\vol 24
\issue 126
\pages 141--149
\mathnet{http://mi.mathnet.ru/vtamu142}
\crossref{https://doi.org/10.20310/1810-0198-2019-24-126-141-149}
\elib{https://elibrary.ru/item.asp?id=38253917}
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  • This publication is cited in the following 1 articles:
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    Russian Universities Reports. Mathematics
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