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This article is cited in 7 scientific papers (total in 7 papers)
An Implicit-Function Theorem for Inclusions
E. R. Avakova, G. G. Magaril-Il'yaevbc a Institute of Control Sciences, Russian Academy of Sciences, Moscow
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
c South Mathematical Institute of VSC RAS
Abstract:
We consider the question of the solvability of an inclusion $F(x,\sigma)\in A$, i.e., of determining a mapping (implicit function) $\sigma\mapsto x(\sigma)$ defined on a set such that $F(x(\sigma),\sigma)\in A$ for any $\sigma$ from this set. Results of this kind play a key role in the different branches of analysis and, especially, in the theory of extremal problems, where they are the main tool for deriving conditions for an extremum.
Keywords:
implicit-function theorem, nonlinear equation, Newton's method, Banach space, multivalued mapping, continuous selector.
Received: 28.09.2010 Revised: 13.01.2011
Citation:
E. R. Avakov, G. G. Magaril-Il'yaev, “An Implicit-Function Theorem for Inclusions”, Mat. Zametki, 91:6 (2012), 813–818; Math. Notes, 91:6 (2012), 764–769
Linking options:
https://www.mathnet.ru/eng/mzm9383https://doi.org/10.4213/mzm9383 https://www.mathnet.ru/eng/mzm/v91/i6/p813
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Abstract page: | 640 | Full-text PDF : | 325 | References: | 44 | First page: | 20 |
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