Holomorphic mappings of the unit disc into itself with two fixed points

被引：23

作者：

Goryainov, V. V. ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2017年 / 208卷 / 03期

关键词：

holomorphic mapping; fixed point; domain of univalence; angular derivative; coefficient region;

D O I：

10.1070/SM8802

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is concerned with holomorphic mappings of the unit disc into itself with two fixed points. Two cases are considered: when one fixed point lies inside the disc and the other lies on the boundary and when both fixed points lie on the boundary. The effect that angular derivatives at boundary fixed points have on the properties of functions inside the unit disc is studied. Conditions on the angular derivatives to guarantee the existence of domains of univalence inside the unit disc are given. The effect of the angular derivatives on the values of the Taylor coefficients of functions is also examined. Bibliography: 19 titles.

引用

页码：360 / 376

页数：17

共 19 条

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SBORNIK MATHEMATICS, 2015, 206 (01) :33-60

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