This article is cited in 3 scientific papers (total in 3 papers)
Two-sided estimates for domains of univalence for classes of holomorphic self-maps of a disc with two fixed points
O. S. Kudryavtsevaa, A. P. Solodovb
a Volgograd State Technical University, Volgograd, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
We investigate the class of holomorphic maps of a disc into itself that have an interior and a boundary fixed point, as well as the class of holomorphic maps of a half-plane into itself that have a fixed point in the interior of the domain and a fixed point at infinity. Two-sided estimates for domains of univalence are obtained for these function classes in terms of the values of the angular derivative at the boundary fixed point and the position of the interior fixed point.
Bibliography: 21 titles.
holomorphic map, fixed points, angular derivative, domain of univalence.
|Ministry of Education and Science of the Russian Federation
|The research of A. P. Solodov was supported by the Russian Federation President grant for the state support of the leading scientific schools of the Russian Federation (grant no. NSh-6222.2018.1).
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Sbornik: Mathematics, 2019, 210:7, 1019–1042
Received: 01.03.2018 and 25.08.2018
O. S. Kudryavtseva, A. P. Solodov, “Two-sided estimates for domains of univalence for classes of holomorphic self-maps of a disc with two fixed points”, Mat. Sb., 210:7 (2019), 120–144; Sb. Math., 210:7 (2019), 1019–1042
Citation in format AMSBIB
\by O.~S.~Kudryavtseva, A.~P.~Solodov
\paper Two-sided estimates for domains of univalence for classes of holomorphic self-maps of a~disc with two fixed points
\jour Mat. Sb.
\jour Sb. Math.
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O. S. Kudryavtseva, A. P. Solodov, “Dvustoronnyaya otsenka oblastei odnolistnosti golomorfnykh otobrazhenii kruga v sebya s invariantnym diametrom”, Izv. vuzov. Matem., 2019, no. 7, 91–95
A. P. Solodov, “Strengthening of Landau's Theorem for Holomorphic Self-Mappings of a Disk with Fixed Points”, Math. Notes, 108:4 (2020), 626–628
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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