| A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α |
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| 引用本文： | 刘小松,冯淑霞.A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α[J].数学季刊,2009,24(2):310-316. |
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| 作者姓名： | 刘小松 冯淑霞 |
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| 作者单位： | |
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| 基金项目： | the National Natural Science Foundation of China，Guangdong Natural Science Foundation，the doctoral foundation of Zhanjiang Normal University |
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| 摘 要： | Suppose f is a spirallike function of type β and order α on the unit disk D.let Ωn,p1,p2,…,pn={z=(z1,z2,…,zn)'∈Cn:nΣj=1|zj|pj<1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers. In this paper,we will prove that Фn,β2,у2…βn,уn(f)(z)=(f(z1),(f(z1)z1)β2(f'(z1))у2z2,…,(f(z1)z1)βn(f'(z1))уnzn)' Preserves spirallikeness of type β and order α on Ωn,p1,p2,…pn.
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| 关 键 词： | spirallike mapping of type β and order α starlike mapping of order α |
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