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. RAN. Math. Inf. Proc. Upr., 2023, Volume 512,Pages <nobr>96

This article is cited in 1 paper

MATHEMATICS

Estimate for domain of univalence on the class of holomorphic self-maps of a disc with two boundary fixed points

V. V. Goryainov^a, O. S. Kudryavtseva^bc, A. P. Solodov^b

^a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russian Federation
^b Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
^c Volgograd State Technical University, Volgograd, Russian Federation

Abstract: Holomorphic self-maps of the unit disc with two boundary fixed points, one of which is a Denjoy–Wolff point are investigated. An upper estimate for domain of univalence is obtained for functions in such class, which depends on the value of the angular derivative at the repulsive boundary fixed point.

Keywords: holomorphic map, fixed points, Denjoy–Wolff theorem, angular derivative, domain of univalence.

UDC: 517.54

Presented: B. S. Kashin
Received: 30.03.2023
Revised: 14.06.2023
Accepted: 14.07.2023

DOI: 10.31857/S2686954323600192