分担集合的亚纯函数族的正规性

Normality of Meromorphic Functions Shared Sets

本文对涉及到高阶导数和分担集合的亚纯函数族的正规性进行了研究,当函数与该函数的高阶导函数分担两个集合,并且函数零点的重级满足一定的条件,以及函数的高阶导函数所组成的函数族内闭一致有界时,亚纯函数族是正规的。在前人研究的基础上,本文又进行了进一步的探索,得到了下面的定理:设F是单位圆盘Δ上的一族亚纯函数S_(1)={a_(1),a_(2)},S_(2)={b_(1),b_(2)},a_(1),a_(2)是两个互相判别的有穷复数,b_(1),b_(2)也是两两互不相同的有限复数,k(≥2)是整数,若对于■f∈F,f^((z))∈S_(1)■f^((k))(z)∈S_(2),f(z)-a_(j)的零点重级至少是k(j=1,2),且{f^((k))(z)|k≥2}在Δ上内闭一致有界,则F在Δ上正规。

In this paper,the normality of meromorphic functions involving higher derivatives and shared sets is studied.The meromorphic function is normal when the function shares two sets with the higher-order derivative of the function,the double level of the function zero satisfies certain conditions,and the function family formed by the higher-order derivative of the function is uniformly closed bounded.On the basis of previous studies,this paper further explores and obtains the following theorems:is a family of meromorphic functions on the unit disk,S_(1)={a_(1),a_(2)},S_(2)={b_(1),b_(2)},a_(1),a_(2) are different and limited,b_(1),b_(2) are different and limited,k(≥2) is integer,if ■f∈F,f^((z))∈S_(1)■f^((k))(z)∈S_(2) the zeros of f(z)-a_(j) have multiplicity at least k(j=1,2),{f^((k))(z)|k≥2} is internally closed uniform bound on the unit circle,is normal on the unit circle.