| 与例外函数和分担函数相关的亚纯函数的正规族 |
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| 引用本文： | 陈俊凡.与例外函数和分担函数相关的亚纯函数的正规族[J].数学学报,2010,53(4):655-662. |
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| 作者姓名： | 陈俊凡 |
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| 作者单位： | 福建师范大学数学与计算机科学学院数学系 福州 350108 |
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| 基金项目： | 国家自然科学基金资助项目(10771076);广东省自然科学基金资助项目(07006700) |
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| 摘 要： | 设F为区域D内的一族亚纯函数,对于每个f∈F,f的所有极点重数至少是2,a(z)和b(z)为两个在D内满足a(z)■b(z)的全纯函数.若对于每个f∈F,f(z)≠a(z)和f(z)≠b(z),则F在D内正规.这个结果改进了经典的Montel定则.此外,我们也讨论了亚纯函数族中每个函数与其导函数分担两个全纯函数的正规性.
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| 关 键 词： | 亚纯函数 正规族 例外函数与分担函数 |
| 收稿时间： | 2008-06-10 |
| 修稿时间： | 2010-01-20 |
Normal Families of Meromorphic Functions Concerning Exceptional Functions and Shared Functions |
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| Institution: | Department of Mathematics, School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou 350108, P. R. China |
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| Abstract: | Let F be a family of meromorphic functions in a domain D, all of whose poles are multiple. Let a(z) and b(z) be holomorphic functions in D such that  . If, for every f ∈F, f(z)≠ a(z) and f(z)≠ b(z), then F is normal in D. This improves the classic Montel's normality criterion. Moreover, we discuss the normality of families of meromorphic functions in which every function shares two holomorphic functions with its derivative.
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| Keywords: | meromorphic function normal family exceptional function and shared function |
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