分担集合的亚纯函数正规族

Normal Families of Meromorphic Functions Related to Shared Sets

把亚纯函数正规族与分担值或分担集合结合起来考虑是亚纯函数正规族理论研究的重要课题。利用Nevanlinna理论研究一类涉及分担集合的亚纯函数族的正规性,主要证明了如下的结论:设F={f(z)}是区域D内的一亚纯函数族,a,b,c是三个相互判别的有穷复数,S={a,b},A为有穷正数,如果对于任意的f(z)∈F,有f(z)-c的零点重级至少为1,且满足两个条件:(ⅰ)E_f'(S)?E_f(S),(ⅱ)当f(z)=c时,有|f'(z)|≤A且0 <|f″(z)|≤A,则F在区域D内正规。

It is an important subject for the study of the normal family theory of meromorphic functions to combine the normal families of meromorphic functions with the shared values or the shared sets.Using Nevanlinna theory researched the shared sets of meromorphic function families.In this paper,Main results are as follows：let F={f（z）} be a family of meromorphic functions on domain D , a,b,c is distinct complex numbers, S={a,b} and A is a poor positive number.If for every f（z）∈F , zero magnitude of f（z）-c is at least 1,and（ⅰ） Ef′（S） Ef（S） , （ⅱ）when f（z）=c is,there is ｜f ′（z）｜≤A and 0〈｜f″（z）｜≤A ,then F={f（z）} is normal on domain D .