涉及导函数与分担亚纯函数的正规定则

Normal criteria concerning derivative functions and shared meromorphic functions

针对涉及导函数与分担亚纯函数的正规定则,得到了如下结果:设Ω是区域D内的亚纯函数族,a(z)(≠0)是亚纯函数。若对于任意μ(z)∈Ω满足如下条件:(1)μ(z)≠0;(2)对μ(z)和a(z)的任意公共极点,其在μ(z)中的重级大于或等于在a(z)中的重级;(3)对任意函数对{μ(z),ν(z)}?Ω,μ^((m))(z)和ν^((m))(z)分担a(z),则Ω在D内正规。同时,给出了2个例子来说明条件(1)和(2)的必要性。

Aiming at normal criteria concerning derivative functions and shared meromorphic functions,the result is show ed as follow s.Let Ω and a(z)(≠0)be a family of functions meromorphic and a meromorphic function in D,respectively.If every μ(z)∈Ω satisfies conditions as follows:(1)μ(z)≠0,(2)for each of the same poles of μ(z)and a(z),the multiplicities in μ(z)are greater than or equal to the multiplicities in a(z),(3)for every functions {μ(z),ν(z)}■Ω,μ^(m)(z)and ν^(m)(z)share a(z),then Ω is normal in D.And tw o examples are given to verify the necessity of conditions(1)and(2).