| 涉及导数的一类全纯函数的正规族 |
| |
| 引用本文： | 姜云波.涉及导数的一类全纯函数的正规族[J].数学的实践与认识,2011,41(4). |
| |
| 作者姓名： | 姜云波 |
| |
| 作者单位： | 北京航空航天大学数学与系统科学学院,数学,信息与行为教育部重点实验室,北京,100191 |
| |
| 基金项目： | 国家自然科学基金(10771011) |
| |
| 摘 要： | 主要使用Zalcman引理来研究全纯函数的正规族,得到了如下的结论:令F为|z|<1内的一族全纯函数,n是一个正整数,a,b是两个复数且满足a≠0,∞,b≠∞.若F满足:Ⅰ)■f∈F,如f有零点,则f的零点重级大于等于3;和Ⅱ)当n≥4时,对F的每一对函数G和H,G″-aG~(n,)与H″-aH~n分担b.则F在|z|<1内正规.
|
| 关 键 词： | 全纯函数 正规族 导数 |
Normal Families of A Kind of Holomorphic Functions Concerning Derivatives |
| |
| JIANG Yun-bo.Normal Families of A Kind of Holomorphic Functions Concerning Derivatives[J].Mathematics in Practice and Theory,2011,41(4). |
| |
| Authors: | JIANG Yun-bo |
| |
| Institution: | JIANG Yun-bo (School of Mathematics and Systems Science and LMIB,Beihang University,Beijing 100191,China) |
| |
| Abstract: | In this paper,we mainly use Zalcman lemna to investigate normal families of holomorphic functions,and gets the following results:let F be a family of holomorphic functions in |z|<1,n is a positive integer,a,b are two complex numbers and satisfies a≠0,∞,b≠∞,If F satisfies:(Ⅰ) for■f∈F,if f has zeros,then the multiplicity of zeros of f is greater than or equal to 3;and(Ⅱ)when n≥4,for every pair of functions G and H belong to F,G" - aG~n and H" - aH~n share b.then F is normal in |z|<1. |
| |
| Keywords: | holomorphic function normal family derivative |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
