函数与其导数具有公共值的全纯函数族的正规性  

Normality of a Family of Holomorphic Functions Which Share One Finite Value with Their Derivatives

作　　者：林伟川[1] 杨连中[2] 

机构地区：[1]福建师范大学数学系,福州350007 [2]山东大学数学系,济南250100

出　　处：《数学学报（中文版）》2003年第3期539-544,共6页Acta Mathematica Sinica：Chinese Series

基　　金：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

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.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.

关 键 词：全纯函数 正规族 公共值 

分 类 号：O174.25[理学—数学]