| 函数与其导数具有公共值的全纯函数族的正规性 |
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| 引用本文： | 林伟川,杨连中.函数与其导数具有公共值的全纯函数族的正规性[J].数学学报,2003,46(3):539-544. |
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| 作者姓名： | 林伟川 杨连中 |
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| 作者单位： | 1. 福建师范大学数学系,福州,350007;山东大学数学系,济南,250100
2. 山东大学数学系,济南,250100 |
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| 基金项目： | 国家自然科学基金(19871050)，高等学校博士学科点专项基金，福建省科委资助项目 |
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| 摘 要： | 设F为区域G上的全纯函数族, a,b(≠0)为两有穷复数,n为正整数,本文推广了Miranda定则,证明了:若对任意的f∈F,(a,b)为f与f(n)在G上的IM分担数组,且当f=a时, f'=f(n+1)=b,则F在G中正规.
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| 关 键 词： | 全纯函数 正规族 公共值 |
| 文章编号： | 0583-1431(2003)03-0539-06 |
| 修稿时间： | 2001年1月4日 |
Normality of a Family of Holomorphic Functions Which Share One Finite Value with Their Derivatives |
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| Wei Chuan LIN.Normality of a Family of Holomorphic Functions Which Share One Finite Value with Their Derivatives[J].Acta Mathematica Sinica,2003,46(3):539-544. |
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| Authors: | Wei Chuan LIN |
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| Institution: | Wei Chuan LIN
(Department of Mathematics, Fujian Teachers University, Fuzhou 350007, P. R. China) (Department of Mathematics, Shandong University, Jinan 250100, P. R. China)
Lian Zhong YANG (Department of Mathematics, Shandong University, Jinan 250100, P. R. China) |
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| Abstract: | In this paper, we prove the following result that improves Miranda's Normal Criteria for a family of holomorphic functions. Let F be a family of functions which are holomorphic in a domain G, a, b (≠ 0) be two finte constants, n be an integer, and let, f∈ F, f and f(n) share the pair of values (a,b) IM, and f' = f(n+1) = b when f = a. Then F is normal on G. |
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| Keywords: | Holomorphic function Normal family Shared value |
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