分担值与亚纯函数的正规性

Normal Families and Shared Values of Meromorphic Functions

把亚纯函数的分担值和推广了的球面导数相结合,得到了如下结果:设F是区域D内的亚纯函数族,若F中的任意函数f(∈F)的零点重数至少是k(k是正整数),f=0当且仅当f(k)=0,且当z∈E(1,f(k))时,存在正整数M(<1),使得f(k)(z)1+f(z)k+1≤M则F在D内正规.

In this paper,the author combines shared values of meromorphic functions with spherical derivative extended and proves the following theorem： Let F be a family of meromorphic functions in an area D,all of whose zeros are of multiplicity at least k,k is a positive integer number.If f∈F,f=0 if and only if f^（k）=0,and suppose that there exists a positive integer M（〈1） such that ｜f^（k）（z）｜/1＋｜f（z）｜^k＋1≤M whenever z∈E-（1,f^（k））,then F is normal.