亚纯函数正规族与分担集

doi:10.13371/j.cnki.chin.q.j.m.2015.02.001

数学季刊 ›› 2015, Vol. 30 ›› Issue (2): 159-165.doi: 10.13371/j.cnki.chin.q.j.m.2015.02.001

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亚纯函数正规族与分担集

1. School of Mathematics Science, Xinjiang Normal University 2. School of Mathematics and Information Science, Guangzhou University

收稿日期:2013-03-19 出版日期:2015-06-30 发布日期:2020-11-23
作者简介:TIAN Hong-gen(1957-), male, native of Hanjiang, Jiangsu, a professor of Xinjiang Normal University, engages in complex analysis; CHEN Wei(1988-), male, native of Ruichang, Jiangxi, a student of Xinjiang Normal University, M.S.D., engages in complex analysis and its applications; YUAN Wen-jun(1957-), male, native of Anyue, Sichuan, a professor of Guangzhou University, Ph.D., engages in complex analysis and its applications.
基金资助:
Supported by the National Natural Science Foundation of China(11461070,11271090)； Supported by the Natural Science Foundation of Guangdong Province(S2012010010121)；

Normal Families of Meromorphic Functions and Shared Set

1. School of Mathematics Science, Xinjiang Normal University 2. School of Mathematics and Information Science, Guangzhou University

Received:2013-03-19 Online:2015-06-30 Published:2020-11-23
About author:TIAN Hong-gen(1957-), male, native of Hanjiang, Jiangsu, a professor of Xinjiang Normal University, engages in complex analysis; CHEN Wei(1988-), male, native of Ruichang, Jiangxi, a student of Xinjiang Normal University, M.S.D., engages in complex analysis and its applications; YUAN Wen-jun(1957-), male, native of Anyue, Sichuan, a professor of Guangzhou University, Ph.D., engages in complex analysis and its applications.
Supported by:
Supported by the National Natural Science Foundation of China(11461070,11271090)； Supported by the Natural Science Foundation of Guangdong Province(S2012010010121)；

摘要/Abstract

摘要： In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers bf,c_fsatisfying（i） b_f/c_fis a constant;（ii） min{σ（0,b_f）,σ（0,c_f）,σ（b_f,c_f）} ≥m for some m > 0;（iii） E_f’（S_f）\subseteq E_f（S_f）,where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and[7].

关键词: meromorphic function, shared set, normal family

Abstract: In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers bf,c_fsatisfying（i） b_f/c_fis a constant;（ii） min{σ（0,b_f）,σ（0,c_f）,σ（b_f,c_f）} ≥m for some m > 0;（iii） E_f’（S_f）\subseteq E_f（S_f）,where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and[7].

Key words: meromorphic function, shared set, normal family

中图分类号:

O174.52

田宏根, 陈玮, 袁文俊. 亚纯函数正规族与分担集[J]. 数学季刊, 2015, 30(2): 159-165.

TIAN Hong-gen, CHEN Wei, YUAN Wen-jun. Normal Families of Meromorphic Functions and Shared Set[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(2): 159-165.

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亚纯函数正规族与分担集

Normal Families of Meromorphic Functions and Shared Set

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