中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (3): 103-109.doi: 10.13471/j.cnki.acta.snus.2019.03.013

• 论文 • 上一篇    下一篇

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

汤获,张海燕,牛潇萌   

  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

摘要:

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。

 

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

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.

Key words: lemniscate of Bernoulli, generalized analytic function, third Hankel determinant, upper bound

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