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

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

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

O. S. Kudryavtsevaa, A. P. Solodovb

a Volgograd State Technical University, 28 Lenin Ave., Volgograd, 400005 Russia
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 НШ-6222.2018.1


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

Full text: PDF file (312 kB)
References: PDF file   HTML file

UDC: 517.54
Received: 20.02.2019
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
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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