摘要
本文研究了亚纯函数及其k阶导数分担两个不同集合的亚纯函数族的正规性问题.证明了如下结论:设F是平面区域D上的亚纯函数族,其中函数的零点重数至少为k+1.设S1,S2是两个集合,且|S1|=m,|S2|=n,S2≠{0},这里m,n是正整数.如果任意f(z)∈F,满足f(z)∈S1■f^(k)(z)∈S2,z∈D,则F在区域D上正规.本文的研究结果是对刘晓俊和庞学诚[刘晓俊,庞学诚.分担值与正规族[J].数学学报(中文版),2007,50(2):409-412]2007年研究结果的改进.
In this paper,the authors study the normality of mermorphic function sharing two different sets with its k-th derivative,and prove the following result:Let F be a family of meromorphic functions on the plane domain D、all of whose zeros are of multiplicity at least k+1,and let S_(1),S_(2) be two sets with |S_(x)|=m,|S_(2)|=n,and S_(2)≠{0},where m,n are positive integers.If for each f(z)∈F,f(z)∈ S1 f^((k))(z)∈S_(2) for all z e D,then T is normal on D.This result improved the theorem of Liu and Pang[Liu,X.J.and Pang,X.C.,Shared values and normal families,Acta Math.Sinica(Chin.Ser)、2007,vol.50,no.2,pp.409-412(in Chinese).]in 2007.
作者
刘丹
邓炳茂
方明亮
LIU Dan;DENG Bingmao;FANG Mingliang(College of Mathematics and Informatics,South China Agricultural University,Guangzhou 510642,China;School of Financial Mathematics and Statics,Guangdong University of Finance,Guangzhou 510121,China;Corresponding author.Institute of Science,Hangzhou Dianzi University,Hangzhou 310018,China.)
出处
《数学年刊(A辑)》
CSCD
北大核心
2023年第1期71-82,共12页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.12171127,No.11701818)的资助。
关键词
正规性
亚纯函数
分担集合
Normality
Meromorphic function
Shared sets