| 刘 丹,邓炳茂,方明亮.分担集合的亚纯函数的正规性*[J].数学年刊A辑,2023,44(1):71~82 |
| 分担集合的亚纯函数的正规性* |
| Normality of Meromorphic Functions Concerning Shared Sets |
| Received:February 23, 2021 Revised:January 19, 2022 |
| DOI：10.16205/j.cnki.cama.2023.0006 |
| 中文关键词: 正规性, 亚纯函数, 分担集合 |
| 英文关键词:Normality, Meromorphic function, Shared sets |
| 基金项目:国家自然科学基金 (No.12171127, No.11701818) |
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| 中文摘要: |
| 本文研究了亚纯函数及其 k 阶导数分担两个不同集合的亚纯函数族的正规性问题.证明了如下结论: 设 F 是平面区域 D上的亚纯函数族, 其中函数的零点重数至少为 k+1. 设S1, S2是两个集合,且|S1|=m, |S2|=n, S2 ≠ 0, 这里m, n是正整数. 如果任意f(z) ∈ F,满足f(z) ∈ S1?f(k)(z) ∈ S2, z ∈ D, 则 F 在区域 D 上正规.本文的研究结果是对刘晓俊和庞学诚[刘晓俊, 庞学诚. 分担值与正规族 [J].数学学报(中文版),2007, 50(2):409--412] 2007年研究结果的改进. |
| 英文摘要: |
| In this paper, the authors study the normality of mermorphic function sharing two different sets with its k-th derivative, and prove the following result: Let F be a family of meromorphic functions on the plane domain D, all of whose zeros are of multiplicity at least k + 1, and let S1, S2 be two sets with |S1| = m, |S2| = n, and S2 ≠ {0},where m, n are positive integers. If for each f(z) ∈ F, f(z) ∈ S1 f(k) (z) ∈ S2 for all z ∈ D, then F is normal on D. This result improved the theorem of Liu and Pang [Liu,X. J. and Pang, X. C., Shared values and normal families, Acta Math. Sinica (Chin. Ser.),2007, vol. 50, no. 2, pp. 409–412 (in Chinese).] in 2007. |
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