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Sbornik: Mathematics, 2020, Volume 211, Issue 11, Pages 1592–1611
DOI: https://doi.org/10.1070/SM9367 (Mi sm9367) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Asymptotically sharp two-sided estimate for domains of univalence of holomorphic self-maps of a disc with an invariant diameter

O. S. Kudryavtsevaab, A. P. Solodovca

a Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
b Volgograd State Technical University, Volgograd, Russia
c Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
English version PDF (534 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM9367
Abstract: Holomorphic self-maps of the unit disc with two fixed diametrically opposite boundary points and an invariant diameter are investigated. Asymptotically sharp estimates for domains of univalence are obtained for functions in such classes, which depend on the product of the angular derivatives at the boundary fixed points.
Bibliography: 16 titles.
Keywords: holomorphic map, fixed points, angular derivative, domain of univalence.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00584-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 20-01-00584-a).
Received: 30.12.2019 and 07.08.2020
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 11, Pages 96–117
DOI: https://doi.org/10.4213/sm9367
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 30C45, 30C55
Language: English
Original paper language: Russian
Citation: O. S. Kudryavtseva, A. P. Solodov, “Asymptotically sharp two-sided estimate for domains of univalence of holomorphic self-maps of a disc with an invariant diameter”, Mat. Sb., 211:11 (2020), 96–117; Sb. Math., 211:11 (2020), 1592–1611
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v211/i11/p96
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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