涉及微分多项式的亚纯函数正规定则
The Normality Criteria of Meromorphic Functions Concerning Differential Polynomial
杨喜龙 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
研究关于微分多项式的亚纯函数的正规定则,利用了Pang-Zalcman引理,将危合文和张惠玲的一些结果进行推广,得到了关于微分多项式以及分担值的亚纯函数的正规定则的结果.设F是定义在区域D上的一个亚纯函数族,若对于任一的 f∈F,f 的零点重级≥k+1,并且满足 f+a(L(f))n ≠b(z),n≥k+2,其中k,n均为正整数,a≠0 为常数,b(z)≠0 在区域D内解析,则F 在区域D内正规.设F 是定义在区域D内的一族亚纯函数,族中任一函数的零点重级≥k+1,a,b 均为非零有穷复数.任一取 f,g∈F,若 f+a(L(f))n,g+a(L(g))n分担b,n,k∈N*,并且n≥2,则F在区域D内正规.
Abstract
In this paper,the regular rule for meromorphic functions of differential polynomials are studied.The Pang-Zalcman Lemma is used to generalize some of the results of Wei Hewen and Zhang Huiling,the results of the higher-order derivatives to differential polynomials and some differential polynomials and meromorphic functions with shared values are obtained.LetFbe a normal of meromorphic functions on domainD,if for each functionf∈F,all of whose zeros multiplicity at leastk+1,f+a(L(f))n ≠b(z),n≥k+2,k,nbe two positive integers,a≠0 be a constant,letb(z)be analytic functions inD,whereb(z)≠0,thenFis normal inD.letFbe a normal of meromorphic functions on domainD,all of whose zeros multiplicity at leastk+1,a≠0,b≠0 be two finite complex numbers.If for each functionf,g∈F,f+a(L(f))n andg+a(L(g))n share the valueb,n,k∈N*,n≥2,thenFis normal in D.
关键词
亚纯函数/微分多项式/正规定则/分担值Key words
meromorphic function/differential polynomial/normal criterion/share value引用本文复制引用
出版年
2024
NETL
NSTL
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