涉及微分多项式的亚纯函数的正规定则

研究了亚纯函数族的正规性,推广了涉及导数的亚纯函数族的正规定则,得到了涉及微分多项式的亚纯函数正规族的一个结果.即:设F为单位圆盘上的一族亚纯函数,a为任一非零有穷复数,k为一正整数.若对任意的f(z)∈F,f(z)的零点重级至少为k+1,极点重级至少为2,且L(f)(z)和f(z)IM分担a,则F在单位圆盘上正规.

Normal Criterion of Meromorphic Functions Concerning Differential Polynomial and Shared Values

The normality of families of meromorphic functions was studied,and a result for normal families of meromorphic functions concerning differential polynomial was obtained,which was extended from a normal criterion on families of meromorphic functions concerning derivative.The novel theorm shows that: Let F be a class of meromorphic functions in the unit circle,a be a nonzero finite plural,and k be a positive integer,if for every f(z)∈F,the multiplicity of zero point is at least k+1,the multiplicity of pole point is at least 2,and a is the IM shared value of L(f)(z) and f(z),then F is normal in the unit circle.