Some Remarks on Schwarz Lemma at the Boundary

被引：12

作者：

Akyel, Tugba ^{[1
]}

Ornek, Bulent Nafi ^{[1
,2
]}

机构：

[1] Gebze Tech Univ, Dept Math, TR-41400 Gebze, Turkey

[2] Amasya Univ, Dept Comp Engn, TR-05100 Merkez Amasya, Turkey

来源：

FILOMAT | 2017年 / 31卷 / 13期

关键词：

Holomorphic function; Schwarz lemma on the boundary; Angular limit; Angular derivative; INEQUALITY;

D O I：

10.2298/FIL1713139A

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a boundary version of the Schwarz lemma is investigated. We consider a function f holomorphic in the unit disc D, f(a) = b, broken vertical bar a broken vertical bar < 1 and broken vertical bar f(z) - alpha broken vertical bar < alpha for z is an element of D, where a is a positive real number and 1/2 < alpha <= 1. We obtain sharp lower bounds on the angular derivative f'(c) at the point c, where f(c) = 2 alpha, broken vertical bar c broken vertical bar = 1.

引用

页码：4139 / 4151

页数：13

共 16 条

[1]

[Anonymous], 1992, GRUNDLEHREN MATH WIS

[2] A refined Schwarz inequality on the boundary [J].