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

doi:10.13471/j.cnki.acta.snus.2019.03.013

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

更新时间：2023-12-11

- Third Hankel determinant for a class of generalized analytic functions onthe righthalf bounded domain of lemniscate of Bernoulli
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 58, Issue 3, Pages: 103-109(2019)
- 作者机构：
  
  赤峰学院数学与统计学院,内蒙古,赤峰,024000
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2019.03.013
  CLC：
- Published：2019，
  
  Published Online：25 May 2019，
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TANG Huo, ZHANG Haiyan, NIU Xiaomeng. Third Hankel determinant for a class of generalized analytic functions onthe righthalf bounded domain of lemniscate of Bernoulli. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 58(3):103-109(2019)
DOI：

TANG Huo, ZHANG Haiyan, NIU Xiaomeng. Third Hankel determinant for a class of generalized analytic functions onthe righthalf bounded domain of lemniscate of Bernoulli. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 58(3):103-109(2019) DOI： 10.13471/j.cnki.acta.snus.2019.03.013.

摘要

设

表示在单位圆盘

={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*

：SR*

={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*

的三阶Hankel行列式 H

(1)，得到其上界估计。

Abstract

Let

be the class of analytic functions

f(z)

 in the unit disc

={z:|z|

1} normalized by f(0)=f′(0)-1=0 . A class of generalized analytic functions SR*

on the right-half bounded domain of lemniscate of Bernoulli is introduced

which is shown as follows:SR*

∈A:(1－λ)f(z)/z+λ

′(z)

√(1+z)(0≤λ≤1;z∈D)}。 .And

the third Hankel determinant H

(1) for the above function class SR*

is investigated and the upper bound for the above determinantH

(1) is obtained.

关键词

伯努利双纽线广义解析函数三阶Hankel行列式上界估计

Keywords

lemniscate of Bernoulligeneralized analytic functionthird Hankel determinantupper bound

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