涉及一类全纯函数复合的正规定则

On the normality of a class of compound holomorphic functions

研究了一类全纯函数族的正规性.证明了结论:设F是区域D内的一族全纯函数,p(z)=(anzn+an-1zn-1+…+a0)/(bmzm+bm-1zm-1+…+b0)是一个满足m+1<n,an≠0,bm≠0的有理函数.若对F中的任意函数f,复合函数p(f(z))≠h(z),h(z)为非常数全纯函数或者当h(z)为常数函数时p(z)-h(z)至少有两个判别的零点,则F在D内正规.这一结果对文献[1]中p(z)是次数≥2的多项式的结果进行了改进.

The normality of a class of holomorphic functions was dealt with and the following result was achieved： let F be a family of analytic functions in a domain D and p （z） = an^z^n＋an-1z^n-1＋…＋a0/bm^z^m＋bm-1z^m-1＋…b0 a holomorphic function with m＋1〈n,an≠0,bm≠0. Suppose that h （z）is either a nonconstant analytic function or a constant function such that p （z） - h （ z ） has at least two distinct roots. If p（f（z））≠h（z） for each f（z）∈ F,then F is normal in D. This result improves the Fang and Yuan＇s result.