关于f+a(L(f))n的正规定则
The Normality Criteria About f+a(L(f))n
冉娜 1杨祺1
作者信息
- 1. 新疆师范大学数学科学学院,新疆乌鲁木齐 830017
- 折叠
摘要
在f+a(f(k))n形式的基础上进行改进,将f(k)推广到关于f的微分多项式L(f),使条件更加一般化,推广已有的结论,并通过反证法,结合Zaclman-Pang引理,利用构造辅助函数的方式,分情况讨论并证明了两种关于f+a(L(f))n形式的正规定则.考虑例外值的情形,证明当f+a(L(f))n ≠ b时,亚纯函数族F在区域D上是正规的.考虑分担值的情形,证明若L(f)的零值点不是f(z)的b值点,且对于亚纯函数族F内的任意两个函数f和g,f+a(L(f))n和g+a(L(g))n分担b,则F在区域D上正规.
Abstract
This paper improves on the form of f +a(f(k))n,and extendf(k)to the differential polynomial L(f)about f.generalize the conditions to the differential polynomials,generalize the existing results,and by using the method of disproving,combine with the Zaclman-pang lemma,in this paper,two normal rules of form f +a(L(f))nare discussed and proved by constructing auxiliary functions.This paper consider the case of exceptional values and obtain that the family of meromorphic functions F is normal in the domain D when f+a(L(f))n≠b.This paper consider the case of shared values and obtain that if the zero of L(f)is not the b-value point of f(z)and for any two functionsfandgin F,f +a(L(f))nand g +a(L(g))nshare b,then F is normal on region D.
关键词
亚纯函数/正规族/微分多项式Key words
meromorphic functions/normal family/differential polynomials引用本文复制引用
出版年
2024
NETL
NSTL
万方数据