数学季刊 >

2015 , Vol. 30 >Issue 2: 159 - 165

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.02.001

亚纯函数正规族与分担集

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

收稿日期: 2013-03-19

  网络出版日期: 2020-11-23

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)；

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Normal Families of Meromorphic Functions and Shared Set

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

Received date: 2013-03-19

  Online published: 2020-11-23

Supported by

Supported by the National Natural Science Foundation of China(11461070,11271090)； Supported by the Natural Science Foundation of Guangdong Province(S2012010010121)；

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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,cf satisfying（i） bf/cf is a constant;（ii） min{σ（0,bf）,σ（0,cf）,σ（bf,cf）} ≥m for some m > 0;（iii） Ef’（Sf）\subseteq Ef（Sf）,where Sf = {bf,cf}.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

本文引用格式

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

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,cf satisfying（i） bf/cf is a constant;（ii） min{σ（0,bf）,σ（0,cf）,σ（bf,cf）} ≥m for some m > 0;（iii） Ef’（Sf）\subseteq Ef（Sf）,where Sf = {bf,cf}.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

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