• 论文 •

### 伯努利双纽线右半有界区域内广义解析函数类的三阶Hankel行列式

1. 赤峰学院数学与统计学院， 内蒙古 赤峰 024000
• 收稿日期:2018-07-16 出版日期:2019-05-25 发布日期:2019-05-25

### Third Hankel determinant for a class of generalized analytic functions onthe righthalf bounded domain of lemniscate of Bernoulli

TANG Huo, ZHANG Haiyan, NIU Xiaomeng

1. School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China
• Received:2018-07-16 Online:2019-05-25 Published:2019-05-25

A 表示在单位圆盘D={z:|z|<1} 内解析且满足 f(0)=f′(0)-1=0 的函数类。首先，引入伯努利双纽线右半有界区域内的广义解析函数类SR*λ：SR*λ={f∈A:(1－λ)f(z)/z+λf′(z)<√(1+z)(0≤λ≤1;z∈D)}。然后，讨论上述函数类 SR*λ 的三阶Hankel行列式 H3(1)，得到其上界估计。

Abstract:

Let A  be the class of analytic functions f(z) in the unit disc D={z:|z|<1} normalized by  f(0)=f′(0)-1=0 . A class of generalized analytic functions SR*λon the right-half bounded domain of lemniscate of Bernoulli is introduced, which is shown as follows:SR*λ={f∈A:(1－λ)f(z)/z+λf′(z)<√(1+z)(0≤λ≤1;z∈D)}。 .
And, the third Hankel determinant H3(1)  for the above function class SR*λ  is investigated and the upper bound for the above determinantH3(1)  is obtained.