E. R. Avakov, G. G. Magaril-Il'yaev, “General Implicit Function Theorem for Close Mappings”, Trudy Mat. Inst. Steklova, 2021, Volume 315,Pages <nobr>7

This article is cited in 4 papers

General Implicit Function Theorem for Close Mappings

E. R. Avakov^a, G. G. Magaril-Il'yaev^bcd

^a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
^b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^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: We prove a sufficiently general implicit function theorem for mappings that are close to an original one in the uniform metric of the space of continuous mappings. As a corollary, we derive an important (for applications) result related to perturbations of linear mappings.

Keywords: implicit function, close mappings, metric regularity.

UDC: 517.51+517.97

Received: February 24, 2021
Revised: April 29, 2021
Accepted: July 12, 2021

DOI: 10.4213/tm4229