纸质出版日期:2019,
网络出版日期:2019-5-25
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设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。
LetAbe the class of analytic functionsf(z) in the unit discD={z:|z|<1} normalized by f(0)=f′(0)-1=0 . A class of generalized analytic functions SR*λon 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*λis investigated and the upper bound for the above determinantH3(1) is obtained.
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