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Mat. Sb., 2019, Volume 210, Number 2, Pages 3–23 (Mi msb9010)  

Hadamard's theorem for mappings with relaxed smoothness conditions

A. V. Arutyunovabc, S. E. Zhukovskiyde

a Lomonosov Moscow State University, Moscow, Russia
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
c V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
d Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia
e RUDN University, Moscow, Russia

Abstract: The paper puts forward sufficient conditions for a mapping from $\mathbb R^n$ to $\mathbb R^n$ to be a global homeomorphism. As an application, the Hadamard theorem for differentiable mappings and conditions for the existence and uniqueness of a coincidence point of a covering mapping and a Lipschitz mapping on $\mathbb R^n$ are derived. Covering mappings of metric spaces and mappings covering at a point are studied.
Bibliography: 23 titles.

Keywords: local homeomorphism, Hadamard's homeomorphism theorem, Caristi-like condition, covering mapping.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.962.2017/4.6
5-100
Russian Foundation for Basic Research 17-51-12064 ННИО_а
18-01-00106-а
19-01-00080-а
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant nos. 17-51-12064 ННИО_а, 18-01-00106-a, 19-01-00080-a) and the “RUDN University Programme 5-100”.


DOI: https://doi.org/10.4213/sm9010

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English version:
Sbornik: Mathematics, 2019, 210:2, 165–183

Bibliographic databases:

Document Type: Article
UDC: 517.275
MSC: 54H25, 34A34, 58C06
Received: 10.09.2017 and 08.10.2018

Citation: A. V. Arutyunov, S. E. Zhukovskiy, “Hadamard's theorem for mappings with relaxed smoothness conditions”, Mat. Sb., 210:2 (2019), 3–23; Sb. Math., 210:2 (2019), 165–183

Citation in format AMSBIB
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