| 关于两类算子的研究 |
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| 引用本文： | 黄盛,贾娜.关于两类算子的研究[J].洛阳师范学院学报,2009,28(5):16-19. |
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| 作者姓名： | 黄盛 贾娜 |
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| 作者单位： | 1. 洛阳师范学院数学科学学院,河南洛阳,471022
2. 天津市大港区油田第四中学,天津,300280 |
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| 摘 要： | 本文给出了用算子Dλf(z)=z(1-z)λ+1*f(z)判别函数为单叶函数的两条判别法则,其中f(z)=z+∑∞k=2akzk,实数λ>-1,符号*为Hadamard卷积,并讨论了两类算子Dλ与Dn间的关系,这里算子Dn定义为D0f(z)=f(z),D1f(z)=Df(z)=zf′(z),Dnf(z)=D(Dn-1f(z)),n∈N.
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| 关 键 词： | 单叶函数 从属 微分算子 |
Two Kinds of Operators |
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| HUANG Sheng,JIA Na.Two Kinds of Operators[J].Journal of Luoyang Teachers College,2009,28(5):16-19. |
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| Authors: | HUANG Sheng JIA Na |
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| Institution: | 1.College of Mathematics and Science;Luoyang Normal University;Luoyang 471022;China;2.The Fourth Middle School in Tianjin Dagang Oilfield;Tianjin 300280;China |
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| Abstract: | This paper demonstrate two discriminant rules of functions being univalent, with operatorf（z）=z＋x∞∑k=2akzk,where Dλf（z）=z/（1-z）λ＋1＊f（z）real number λ 〉 - 1, the symbol ＊ refers to convolution. This paper also discusses the relations between two kinds of operators Dλ and Dn, and here Dn is defined as D0f（z）=f（z）=Df（z）=zf＇（z）,Dnf（z）=D（Dn-1f（z））,n∈N. |
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| Keywords: | univalent functions subordination differential operator |
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