期刊文献+

分担集合的亚纯函数的正规性 被引量:1

Normality of Meromorphic Functions Concerning Shared Sets
下载PDF
导出
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
  • 相关文献

参考文献4

二级参考文献12

  • 1Yang L., Value Distribution Theory, Berlin: Spring-Verlag, 1993. 被引量:1
  • 2Hayman W. K., Meromorphic Functions, Oxford: Clarendon Press, 1964. 被引量:1
  • 3Schwick W., Shaving values and normality, Arch Math., 1992, 59: 50-54. 被引量:1
  • 4Pang X. C., Zalcman L. Norrnality and shared values, Ark. Mat., 2000, 38: 171-182. 被引量:1
  • 5Chang J. M., Fang M. L., Zalcman L., Normality and fixed-points of meromorphic functions, Ark. Mat., 2005, 43: 307-321. 被引量:1
  • 6Liu X. J., Pang X. C., Shared values and normal function, Acta Mathematica Sinica, Chinese Series, 2007, 50(2): 409-412. 被引量:1
  • 7Chang J. M., Wang Y. F., Shared values, Picard values and normality, Tohoku Math. J., 2011, 63:149-162. 被引量:1
  • 8Hayman W. K., Miles J., On the growth of a meromorphic function and its derivatives, Complex Vari., 1989 12: 245-260. 被引量:1
  • 9Pang X. C., Zalcman L., Normal families and shared values, Bull. London Math. Soc., 2000, 32: 325-331. 被引量:1
  • 10庞学诚.BLOCH'S PRINCIPLE AND NORMAL CRITERION[J].Science China Mathematics,1989,32(7):782-791. 被引量:27

共引文献117

同被引文献1

引证文献1

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部