This article is cited in 1 paper

Exact regions of mutual variation of coefficients of holomorphic self-maps of a disc with fixed points

O. S. Kudryavtseva<sup>ab

a</sup> Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics, GSP-1, 1 Leninskie Gory, Moscow, 119991 Russia
^b Volgograd State Technical University, 28 Lenin Ave., Volgograd, 400005 Russia

Abstract: A method is proposed that allows us to obtain the exact regions of mutual variation of Taylor coefficients of holomorphic self-maps of a disc with an interior fixed point and an arbitrary finite set of different boundary fixed points. Based on this method, exact inequalities for the first and second coefficients are obtained.

Keywords: holomorphic mapping, fixed points, angular derivative, coefficient regions.

UDC: 517.54

Received: 28.08.2022
Revised: 28.08.2022
Accepted: 28.09.2022

DOI: 10.26907/0021-3446-2023-5-48-57

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2023, 67:5, 41–49