O. S. Kudryavtseva, A. P. Solodov, “Two-sided estimate of univalence domains of holomorphic mappings of the disc into itself with an invariant diameter”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 7,Pages <nobr>91

This article is cited in 3 papers

Brief communications

Two-sided estimate of univalence domains of holomorphic mappings of the disc into itself with an invariant diameter

O. S. Kudryavtseva^a, A. P. Solodov^b

^a Volgograd State Technical University, 28 Lenin Ave., Volgograd, 400005 Russia
^b Lomonosov Moscow State University, 1 Leninskie Gory str., Moscow, 119991 Russia

Abstract: We obtain an asymptotically sharp two-sided estimate of univalence domains on classes of holomorphic mappings of the unit disc into itself with two boundary fixed points and an invariant diameter. The estimate depends on the value of the product of the angular derivatives at the boundary fixed points.

Keywords: holomorphic mapping, fixed point, angular derivative, domain of univalence.

UDC: 517.54

Received: 20.02.2019
Revised: 20.02.2019
Accepted: 27.03.2019

DOI: 10.26907/0021-3446-2019-7-91-95