关于亚纯函数正规族与分担值

On the normal families and shared values

研究亚纯函数单向分担3个公共值的亚纯函数的正规性.利用在函数极点处构造函数结合Hurwitz定理得到了一个更一般的正规定则.设F是区域D上的亚纯函数族,a≠0,b≠0,c为相互判别的有限复数,M1,M3是2个正数,若f∈F,满足(ⅰ)f′=a→|f-c|≥M1,(ⅱ)f=b→f′=b,(ⅲ)f=c→|f′|≤M3,则F在D上正规.

The normality of meromorphic functions that one-way sharing three values was studied. By using the constructor at the pole of the function and combining with Hurwitz theorem, a more general normal criterion was obtained. Let be a family of meromorphic function on D, a ≠0;b ≠0;c are three distinct nite complex numbers, M1 ,M3 are two positve numbers, if for eachf,it safises （ i ） .f =a=｜f-c｜ ≥M1 ,（ ii ） f=b→f =b,（iii） f=c→｜≤M3 ,then .is normal in D.