| 涉及分担函数与分担值的正规定则 |
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| 引用本文： | 曾翠萍,邓炳茂,方明亮.涉及分担函数与分担值的正规定则[J].数学年刊A辑(中文版),2021,42(1):115-124. |
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| 作者姓名： | 曾翠萍 邓炳茂 方明亮 |
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| 作者单位： | 广东金融学院应用数学系, 广州 510521.;华南农业大学应用数学研究所, 广州 510642. |
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| 基金项目： | 国家自然科学基金 (No.\,11901119)和广东省普通高校特色创新类项目(No.\,2019KTSCX111) |
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| 摘 要： | 研究了涉及分担函数的正规定则,证明了:设F为定义在区域D内的一族亚纯函数,n,k是两个正整数,满足n≥k+3.如果对于F中任意一个函数f,(fn)((k))-z至多有一个不同的零点,则F在D内正规.此结论说明在(fn)((k))具有不动点的情形下,1990年杨乐在Notre Dame大学举行的学术会议上提出的断言仍然成立.
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| 关 键 词： | 亚纯函数 正规族 分担函数 分担值 |
| 收稿时间： | 2017/9/10 0:00:00 |
| 修稿时间： | 2018/3/22 0:00:00 |
Normal Criterion Concerning Shared Functions and Shared Values |
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| ZENG Cuiping,DENG Bingmao,FANG Mingliang.Normal Criterion Concerning Shared Functions and Shared Values[J].Chinese Annals of Mathematics,2021,42(1):115-124. |
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| Authors: | ZENG Cuiping DENG Bingmao FANG Mingliang |
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| Institution: | Department of Applied Mathematics, Guangdong University Of Finance,Guangzhou 510521, China.;Corresponding author. Department of Applied Mathematics, Guangdong University Of Finance, Guangzhou 510521, China.; Institute of Applied Mathematics, South China Agricultural University,Guangzhou 510642, China. |
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| Abstract: | The authors study normal criterion concerning share functions and share values and prove:Let F be a family of meromorphic functions in D,and let k,n be two positive integers with n≥k+3.For each f∈F,(fn)(k)-z has at most one zero,then F is normal in D.It means that the claim made by Yang at the academic conference in University of Notre Dame in 1990 is still valid when(fn)(k)has fixed point. |
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| Keywords: | Meromorphic functions Normal families Shared functions Shared values |
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