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