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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, Volume 160, Book 4, Pages 771–777 (Mi uzku1495)  
Harmonic mappings and finite valency of analytic functions

L. A. Xuanab

a Kazan Federal University, Kazan, 420008 Russia
b Can Tho University of Technology, Can Tho, 900000, Vietnam
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Abstract: The harmonic mappings of a circle into domains that can be cut into a finite number of convex subdomains has been studied. An estimate of the valency of holomorphic mappings of a circle composed of analytical components of the harmonic function has been obtained. In addition, the Keobe harmonic univalent function has been considered to illustrate the results of the research.
Keywords: harmonic function, univalent function, $n$-valent function, convex function, shear construction.
Received: 15.08.2018
Document Type: Article
UDC: 517.54
Language: Russian
Citation: L. A. Xuan, “Harmonic mappings and finite valency of analytic functions”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 160, no. 4, Kazan University, Kazan, 2018, 771–777
Citation in format AMSBIB
\Bibitem{Xua18}
\by L.~A.~Xuan
\paper Harmonic mappings and finite valency of analytic functions
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2018
\vol 160
\issue 4
\pages 771--777
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1495}
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