Abstract:
A class of holomorphic self-mappings of a strip which is symmetric with respect to the real axis is studied. It is required that the mappings should boundedly deviate from the identity transformation on the real axis. Distortion theorems for this class of functions are obtained, and domains of univalence are found that arise for certain values of the parameter characterizing the deviation of the mappings from the identity transformation on the real axis.
Keywords:
holomorphic mapping, fixed point, domains of univalence, angular derivative, distortion theorems.
This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00674-a) and by a grant of the President of the Russian Federation (project no. NSh-9110.2016.1).
Citation:
V. V. Goryainov, “Holomorphic Mappings of a Strip into Itself with Bounded Distortion at Infinity”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Trudy Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 101–111; Proc. Steklov Inst. Math., 298 (2017), 94–103
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\paper Holomorphic Mappings of a Strip into Itself with Bounded Distortion at Infinity
\inbook Complex analysis and its applications
\bookinfo Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 298
\pages 101--111
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3813}
\crossref{https://doi.org/10.1134/S0371968517030074}
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\jour Proc. Steklov Inst. Math.
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Linking options:
https://www.mathnet.ru/eng/tm3813
https://doi.org/10.1134/S0371968517030074
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O. S. Kudryavtseva, A. P. Solodov, “Univalent covering domain for a class of holomorphic self-maps of a disk with two boundary fixed points”, Math. Notes, 116:4 (2024), 858–861
V. V. Goryainov, O. S. Kudryavtseva, A. P. Solodov, “Estimate for domain of univalence on the class of holomorphic self-maps of a disc with two boundary fixed points”, Dokl. Math., 108:1 (2023), 326–330
V. V. Goryainov, O. S. Kudryavtseva, A. P. Solodov, “Iterates of holomorphic maps, fixed points, and domains of univalence”, Russian Math. Surveys, 77:6 (2022), 959–1020
A. P. Solodov, “The exact domain of univalence on the class of holomorphic maps of a disc into itself with an interior and a boundary fixed points”, Izv. Math., 85:5 (2021), 1008–1035
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
O. S. Kudryavtseva, A. P. Solodov, “Two-sided estimate of univalence domains of holomorphic mappings of the disc into itself with an invariant diameter”, Russian Math. (Iz. VUZ), 63:7 (2019), 80–83
V. V. Goryainov, “Loewner-Kufarev equation for a strip with an analogue of hydrodynamic normalization”, Lobachevskii J. Math., 39:6 (2018), 759–766
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