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 Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 7, Pages 91–95 (Mi ivm9486)

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Two-sided estimate of univalence domains of holomorphic mappings of the disc into itself with an invariant diameter

O. S. Kudryavtsevaa, A. P. Solodovb

b Lomonosov Moscow State University, 1 Leninskie Gory str., Moscow, 119991 Russia

Abstract: We obtain an asymptotically sharp two-sided estimate of univalence domains on classes of holomorphic mappings of the unit disc into itself with two boundary fixed points and an invariant diameter. The estimate depends on the value of the product of the angular derivatives at the boundary fixed points.

Keywords: holomorphic mapping, fixed point, angular derivative, domain of univalence.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÍØ-6222.2018.1

DOI: https://doi.org/10.26907/0021-3446-2019-7-91-95

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UDC: 517.54
Revised: 20.02.2019
Accepted: 27.03.2019

Citation: O. S. Kudryavtseva, A. P. Solodov, “Two-sided estimate of univalence domains of holomorphic mappings of the disc into itself with an invariant diameter”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 7, 91–95

Citation in format AMSBIB
\Bibitem{KudSol19} \by O.~S.~Kudryavtseva, A.~P.~Solodov \paper Two-sided estimate of univalence domains of holomorphic mappings of the disc into itself with an invariant diameter \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2019 \issue 7 \pages 91--95 \mathnet{http://mi.mathnet.ru/ivm9486} \crossref{https://doi.org/10.26907/0021-3446-2019-7-91-95} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. 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”, Sb. Math., 211:11 (2020), 1592–1611
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