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Sbornik: Mathematics, 2019, Volume 210, Issue 7, Pages 1019–1042
DOI: https://doi.org/10.1070/SM9095 (Mi sm9095) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Two-sided estimates for domains of univalence for classes of holomorphic self-maps of a disc with two fixed points

O. S. Kudryavtsevaa, A. P. Solodovb

a Volgograd State Technical University, Volgograd, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
English version PDF (609 kB) Citations (14)
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DOI: https://doi.org/10.1070/SM9095
Abstract: We investigate the class of holomorphic maps of a disc into itself that have an interior and a boundary fixed point, as well as the class of holomorphic maps of a half-plane into itself that have a fixed point in the interior of the domain and a fixed point at infinity. Two-sided estimates for domains of univalence are obtained for these function classes in terms of the values of the angular derivative at the boundary fixed point and the position of the interior fixed point.
Bibliography: 21 titles.
Keywords: holomorphic map, fixed points, angular derivative, domain of univalence.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-6222.2018.1
The research of A. P. Solodov was supported by the Russian Federation President grant for the state support of the leading scientific schools of the Russian Federation (grant no. NSh-6222.2018.1).
Received: 01.03.2018 and 25.08.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 7, Pages 120–144
DOI: https://doi.org/10.4213/sm9095
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: English
Original paper language: Russian
Citation: O. S. Kudryavtseva, A. P. Solodov, “Two-sided estimates for domains of univalence for classes of holomorphic self-maps of a disc with two fixed points”, Mat. Sb., 210:7 (2019), 120–144; Sb. Math., 210:7 (2019), 1019–1042
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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