一个涉及亚纯函数的正规定则

journal6 ›› 2009, Vol. 30 ›› Issue (1): 13-16.

一个涉及亚纯函数的正规定则

（1.湖南农业大学理学院应用数学系，湖南长沙 410128；2.中华女子学院基础部，北京 00101）

出版日期:2009-01-25 发布日期:2012-04-27

A Normality Criterion of Meromorphic Functions

(1.Dept. of Applied Math.,College of Science,Hunan Agricultural University,Changsha 410128,China;2.Basic Department,China Woman’s University,Beijing 100101,China)

Online:2009-01-25 Published:2012-04-27
About author:WANG You-ming(1973-),male,was born in Shaoyang City,Hunan Province,lecturer;engages in complex analysis.
Supported by:
Supported by the NSF of Hunan Province (06C417)

摘要/Abstract

摘要：假设F是区域DC的亚纯函数族，又设k是一个正整数，a,b(≠a),c(≠a)是3个有限复数且h1,h2,h3是3个正数.若对每个函数f∈F有f(z)=a｜f(k)(z)｜≤h1,f(z)=b｜f(k)(z)｜≤h2,f(k)(z)=c｜f(z)｜≥h3,且f所有的零点的重级不小于k，则F在D内正规.

关键词： 亚纯函数, 正规性

Abstract: Let F be a family of meromorphic functions in a domain DC,all of whose zeros are of multiplicity at least k.Let k be a positive integer,and let a,b and c be three finite complex numbers such that a≠b,a≠c and h1,h2,h3 be three positive numbers.If f(z)=a |f(k)(z)|≤h1,f(z)=b  |f(k)(z)|≤h2,f(k)(z) =c|f(z)|≥h3 for every f∈F,and all f’s zeros are of multiplicity at least k,then F is normal in D.

Key words: meromorphic function, normality

王有明, 腾静. 一个涉及亚纯函数的正规定则[J]. journal6, 2009, 30(1): 13-16.

WANG You-Ming, TENG Jing. A Normality Criterion of Meromorphic Functions[J]. journal6, 2009, 30(1): 13-16.

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