| 摘要: |
| 讨论2个亚纯函数族涉及分担值的正规性,证明如下结论:设F和G为区域D上的2个亚纯函数族,a1,a2,a3为3个互不相同的复数,k ≥ 1,l ≥ 0为整数.若亚纯函数族G正规,且对G的任意子列gn(z),有gn→g,且g≢∞;若对任意的f∈F,零点重数大于等于k+1,且存在g∈G,使得f(k)(z)和g(l)(z)分担a1,a2,a3,则F在D上正规. |
| 关键词: 亚纯函数 正规族 分担值 |
| DOI： |
| 投稿时间：2013-09-30修订日期：2013-12-11 |
| 基金项目:陕西铁路工程职业技术学院科研基金项目(2013-12)资助。 |
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| Normal Criteria about Two Families of Meromorphic Functions Involving Shared Values |
|
LI Yun-tong1, LAI Li-ping2
|
| (1.Department of Basic Courses, Shaanxi Railway Institute, Weinan, Shaanxi, 714000, China;2.Management College of China West Normal University, Nanchong, Sichuan, 637000, China) |
| Abstract: |
| We mainly discuss the normality of two families of meromorphic functions involving shared values, which was proved as follows:Let F and G be two families of functions meromorphic on a domain D.Let a1, a2, a3 be three distinct complex numbers, k ≥ 1, l ≥ 0 be two integers. If G is normal, and for any subsequence {gn(z)} of G, gn→g, we have g≢∞ on D.If for every f∈F, all zeros of f(z) are of multiplicity at least k+1 in D, there exists g∈G such that f(k)(z) and g(l)(z) share the values a1, a2, a3, then F is normal on D. |
| Key words: meromorphic functions normal family shared value |
