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| 全纯函数的分担值与正规族 | |
| 引用本文： | 李江涛,仪洪勋. 全纯函数的分担值与正规族[J]. 高校应用数学学报(英文版), 2006, 21(3): 335-342. DOI: 10.1007/s11766-003-0010-9 |
| 作者姓名： | 李江涛 仪洪勋 |
| 作者单位： | 山东大学;山东大学 |
| 基金项目： | 山东大学校科研和教改项目 , 国家自然科学基金 |
| 摘 要： | Let F be a family of holomorphic functions in a domain D, k be a positive integer, a, b（≠0）, c（≠0） and d be finite complex numbers. If, for each f∈F, all zeros of f-d have multiplicity at least k, f^（k） = a whenever f=0, and f=c whenever f^（k） = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp. |
| 关 键 词： | 晶体函数 常态族 分享价值 有限复形数 数学分析 |
| 收稿时间： | 2005-09-09 |
Normal families and shared values of holomorphic functions |
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| Li Jiangtao,Yi Hongxun. Normal families and shared values of holomorphic functions[J]. Applied Mathematics A Journal of Chinese Universities, 2006, 21(3): 335-342. DOI: 10.1007/s11766-003-0010-9 | |
| Authors: | Li Jiangtao Yi Hongxun |
| Affiliation: | (1) Department of Mathematics, Shandong University, 250100 Shandong, China;(2) Department of Mathematics, Chongqing University, 400044 Chongqing, China |
| Abstract: | Let F be a family of holomorphic functions in a domain D, k be a positive integer,a, b(≠ 0), c(≠ 0) and d be finite complex numbers. If, for each f ∈ F, all zeros of f - d have multiplicity at least k, f(κ) = a whenever f = 0, and f = c whenever f(κ) = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp. |
| Keywords: | holomorphic function normal family shared value |
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