Some Remarks on Schwarz Lemma at the Boundary

被引：10
|
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
收藏
页码：4139 / 4151
页数：13
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