E. R. Avakov, G. G. Magaril-Il'yaev, “An Implicit Function Theorem for Inclusions Defined by Close Mappings”, Mat. Zametki, 2018, Volume 103, Issue 4,Pages <nobr>483–489</nobr>

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Mat. Zametki, 2018 Volume 103, Issue 4, Pages 483–489 (Mi mzm11576)

This article is cited in 6 papers

An Implicit Function Theorem for Inclusions Defined by Close Mappings

E. R. Avakov^ab, G. G. Magaril-Il'yaev^acd

^a Lomonosov Moscow State University
^b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
^c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
^d Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

Abstract: The paper deals with the question of the solvability of inclusions $F(x,\sigma)\in Q$ for mappings $F$ close, in some metrics, to a given mapping $\widehat{F}$.

Keywords: implicit function, Brouwer's fixed point theorem, Newton's method.

UDC: 517.51

Received: 04.03.2017
Revised: 12.10.2017

DOI: 10.4213/mzm11576

English version: Mathematical Notes, 2018, 103:4, 507–512

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