L. A. Xuan, “Harmonic mappings and finite valency of analytic functions”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, Volume 160, Book 4,Pages <nobr>771

Harmonic mappings and finite valency of analytic functions

L. A. Xuan^ab

^a Kazan Federal University, Kazan, 420008 Russia
^b Can Tho University of Technology, Can Tho, 900000, Vietnam

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.

UDC: 517.54

Received: 15.08.2018