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This article is cited in 2 scientific papers (total in 2 papers)
Implicit Function Theorem in a Neighborhood of an Abnormal Point
A. V. Arutyunova, K. I. Salikhovab a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Abstract:
We study the existence of an implicit function, defined by an equation $G(x,\sigma )=0$, in a neighborhood of an abnormal point $(x_0,\sigma _0)$. We prove that if some $\lambda $-truncation of the mapping $F(x) = G(x,\sigma _0)$ is regular in a certain direction, then the sought implicit function exists.
Received: March 28, 2021 Revised: April 19, 2021 Accepted: July 12, 2021
Citation:
A. V. Arutyunov, K. I. Salikhova, “Implicit Function Theorem in a Neighborhood of an Abnormal Point”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 26–33; Proc. Steklov Inst. Math., 315 (2021), 19–26
Linking options:
https://www.mathnet.ru/eng/tm4228https://doi.org/10.4213/tm4228 https://www.mathnet.ru/eng/tm/v315/p26
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Abstract page: | 289 | Full-text PDF : | 77 | References: | 21 | First page: | 5 |
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