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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 7, Pages 43–51
DOI: https://doi.org/10.26907/0021-3446-2021-7-43-51 (Mi ivm9694) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Inequality of Schwarz type for holomorphic self-maps of a disc with fixed points

O. S. Kudryavtsevaab

a Moscow State University, Moscow Center of Fundamental and Applied Mathematics, GSP-1, 1 Leninskie Gory, Moscow, 119991 Russia
b Volgograd State Technical University, 28 Lenin Ave., Volgograd, 400005 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-7-43-51
Abstract: In the class of holomorphic functions that mapping the unit disc into itself and having an inner and two boundary fixed points, the exact set of the values of derivative at zero in terms of the angular derivatives at the boundary fixed points is given. As a corollary in the class of such functions a disc of univalence with center at zero is found.
Keywords: holomorphic mapping, fixed point, angular derivative, Schwarz inequality, domain of univalence.
Funding agency Grant number
Russian Science Foundation 21-11-00131
Received: 27.06.2020
Revised: 26.04.2021
Accepted: 29.06.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 7, Pages 35–42
DOI: https://doi.org/10.3103/S1066369X21070057
Document Type: Article
UDC: 517.54
Language: Russian
Citation: O. S. Kudryavtseva, “Inequality of Schwarz type for holomorphic self-maps of a disc with fixed points”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 7, 43–51; Russian Math. (Iz. VUZ), 65:7 (2021), 35–42
Citation in format AMSBIB
\Bibitem{Kud21}
\by O.~S.~Kudryavtseva
\paper Inequality of Schwarz type for holomorphic self-maps of a disc with fixed points
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 7
\pages 43--51
\mathnet{http://mi.mathnet.ru/ivm9694}
\crossref{https://doi.org/10.26907/0021-3446-2021-7-43-51}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 7
\pages 35--42
\crossref{https://doi.org/10.3103/S1066369X21070057}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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