Sharp univalent covering domain for the class of holomorphic self-maps of a disc with fixed interior and boundary points

被引：0

作者：

Kudryavtseva, O. S. ^{[1
,2
]}

Solodov, A. P. ^{[1
,2
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow, Russia

[2] Moscow Ctr Fundamental & Appl Math, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2024年 / 215卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

holomorphic map; fixed point; angular derivative; univalence domain; univalent covering domain; ANALYTIC-FUNCTIONS; 2-SIDED ESTIMATE; MAPPINGS; ITSELF; ITERATION; THEOREM;

D O I：

10.4213/sm9901e

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The class of holomorphic maps of the unit disc to itself, with an interior and a boundary fixed point is under consideration. For the class of such functions a sharp univalent covering domain is found in its dependence on the value of the angular derivative at the boundary fixed point and the position of the interior fixed point. This result can be viewed as a refinement of Landau's theorem on the univalent covering disc for the class of bounded holomorphic functions with prescribed derivative at the interior fixed point.

引用

页码：183 / 205

页数：23

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