函数与其导数具有公共值的全纯函数族的正规性

林伟川;杨连中

数学学报 ›› 2003, Vol. 46 ›› Issue (3) : 539-544.

中国科学院数学与系统科学研究院期刊网
数学学报 ›› 2003, Vol. 46 ›› Issue (3) : 539-544. DOI: 10.12386/A2003sxxb0075
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函数与其导数具有公共值的全纯函数族的正规性

    林伟川;杨连中
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Normality of a Family of Holomorphic Functions Which Share One Finite Value with Their Derivatives

    Wei Chuan LIN(1),Lian Zhong YA
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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.

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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全纯函数 / 正规族 / 公共值

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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. 数学学报, 2003, 46(3): 539-544 https://doi.org/10.12386/A2003sxxb0075
Wei Chuan LIN(1),Lian Zhong YA. Normality of a Family of Holomorphic Functions Which Share One Finite Value with Their Derivatives. Acta Mathematica Sinica, Chinese Series, 2003, 46(3): 539-544 https://doi.org/10.12386/A2003sxxb0075

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