关于亚纯函数分担值集正规族的注记

数学季刊 ›› 2011, Vol. 26 ›› Issue (3): 360-365.

关于亚纯函数分担值集正规族的注记

1. Department of Mathematics, Xinjiang Normal University 2. Shaozhou Normal College, Shaoguan University 3. School of Mathematics and Information Science, Guangzhou University

收稿日期:2010-09-03 出版日期:2011-09-30 发布日期:2023-04-18
作者简介:XIAO Bing(1960-), male, native of Urumgi, Xinjiang, a lecturer of Xinjiang Normal University, M.S.D., engages in complex analysis and its applications; WU Qi-feng(corresponding author)(1963-), male, native of Shaoguan, Guangdong, an associate professor of Shaoguan University, M.S.D., engages in complex analysis and statistics; 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 NSF of China(10771220)； Supported by the Doctorial Point Fund of National Education Ministry of China(200810780002)；

A Note on Normal Families of Meromorphic Functions and Sharing Set

1. Department of Mathematics, Xinjiang Normal University 2. Shaozhou Normal College, Shaoguan University 3. School of Mathematics and Information Science, Guangzhou University

Received:2010-09-03 Online:2011-09-30 Published:2023-04-18
About author:XIAO Bing(1960-), male, native of Urumgi, Xinjiang, a lecturer of Xinjiang Normal University, M.S.D., engages in complex analysis and its applications; WU Qi-feng(corresponding author)(1963-), male, native of Shaoguan, Guangdong, an associate professor of Shaoguan University, M.S.D., engages in complex analysis and statistics; 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 NSF of China(10771220)； Supported by the Doctorial Point Fund of National Education Ministry of China(200810780002)；

摘要/Abstract

摘要： In the paper, we prove the main result: Let k(≥2) be an integer, and a, b and c be three distinct complex numbers. Let F be a family of functions holomorphic in a domain D in complex plane, all of whose zeros have multiplicity at least k. Suppose that for each f∈F, f(z) and f(k)(z) share the set {a,b,c}. Then F is a normal family in D.

关键词: entire function, normal family, meromorphic function, share value set

Abstract: In the paper, we prove the main result: Let k(≥2) be an integer, and a, b and c be three distinct complex numbers. Let F be a family of functions holomorphic in a domain D in complex plane, all of whose zeros have multiplicity at least k. Suppose that for each f∈F, f(z) and f(k)(z) share the set {a,b,c}. Then F is a normal family in D.

Key words: entire function, normal family, meromorphic function, share value set

中图分类号:

O174.52

肖冰, 吴奇峰, 袁文俊. 关于亚纯函数分担值集正规族的注记[J]. 数学季刊, 2011, 26(3): 360-365.

XIAO Bing, WU Qi-feng, YUAN Wen-jun. A Note on Normal Families of Meromorphic Functions and Sharing Set[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(3): 360-365.

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