分担值与亚纯函数的正规性

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)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.

Normal Families and Shared Values of Meromorphic Functions

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.