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 Mat. Sb., 2020, Volume 211, Number 11, Pages 96–117 (Mi msb9367)

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
c Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

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-à This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 20-01-00584-a).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9367

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English version:
Sbornik: Mathematics, 2020, 211:11, 1592–1611

UDC: 517.54
MSC: 30C45, 30C55

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
\Bibitem{KudSol20} \by O.~S.~Kudryavtseva, A.~P.~Solodov \paper Asymptotically sharp two-sided estimate for domains of univalence of holomorphic self-maps of a~disc with an invariant diameter \jour Mat. Sb. \yr 2020 \vol 211 \issue 11 \pages 96--117 \mathnet{http://mi.mathnet.ru/msb9367} \crossref{https://doi.org/10.4213/sm9367} \transl \jour Sb. Math. \yr 2020 \vol 211 \issue 11 \pages 1592--1611 \crossref{https://doi.org/10.1070/SM9367}