| 一个涉及亚纯函数的正规定则 |
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| 引用本文： | 王有明,腾静.一个涉及亚纯函数的正规定则[J].吉首大学学报(自然科学版),2009,30(1):13-16. |
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| 作者姓名： | 王有明 腾静 |
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| 作者单位： | （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） |
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| 摘 要： | 假设F是区域DC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.
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| 关 键 词： | 亚纯函数 正规性 |
A Normality Criterion of Meromorphic Functions |
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| WANG You-ming,TENG Jing.A Normality Criterion of Meromorphic Functions[J].Journal of Jishou University(Natural Science Edition),2009,30(1):13-16. |
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| Authors: | WANG You-ming TENG Jing |
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| Institution: | (1.Dept. of Applied Math.,College of Science,Hunan Agricultural University,Changsha 410128,China;2.Basic Department,China Woman’s University,Beijing 100101,China) |
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| Abstract: | Let F be a family of meromorphic functions in a domain D C C, all of whose zeros are of multi-plicity 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 nor-mal in D. |
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| Keywords: | meromorphic function normalityCLC number O174 52 Document code A |
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