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
b Volgograd State Technical University, Volgograd, Russia
c Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
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.
holomorphic map, fixed points, angular derivative, domain of univalence.
|Russian Foundation for Basic Research
|This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 20-01-00584-a).
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Sbornik: Mathematics, 2020, 211:11, 1592–1611
MSC: 30C45, 30C55
Received: 30.12.2019 and 07.08.2020
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
\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.
\jour Sb. Math.
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