与分担值相关亚纯函数的正规性

Normality of Meromorphic Functions on Shared Values

利用Nevanlinna理论研究一类涉及分担函数的亚纯函数族的正规性,得到一个与分担函数相关的正规定则.设k是一个正整数,F是区域D内的亚纯函数族.若对任意的f∈F,其零点重级至少为k,且满足:1)f(z)=0f(k)(z)+∑i=1kbi(z)f(k-i)(z)=a(z);2)f(k)(z)+∑i=1kbi(z)f(k-i)(z)=a(z)■0<|f(k+1)(z)+b1(z)f(k)(z)-a′(z)|<|a(z)|.其中a(z)(a(z)≠0),bi(z)(i=1,2,…,k)是区域D内的全纯函数.则F在区域D内正规.

We studied the normality of the family of meromorphic functions about sharing functions using Nevanlinna theory method,obtaining a normal criterion.Let k be a positive integer,F be a family of meromorphic functions on a domain D.For each f∈F,all its zeros have multiplicity,at least,k.If 1）f（z）=0f（k）（z）＋∑i=1kbi（z）f（k-i）（z）=a（z）;2）f（k）（z）＋∑i=1kbi（z）f（k-i）（z）=a（z）■0｜f（k＋1）（z）＋b1（z）f（k）（z）-a′（z）｜｜a（z）｜,where a（z）（a（z）≠0）,bi（z）（i=1,2,…,k）are holomorphic functions on D,then Fis normal on D.