| Roper-Suffridge算子上的偏差定理下界估计的简单证明 |
| |
| 引用本文： | 王建飞,刘太顺. Roper-Suffridge算子上的偏差定理下界估计的简单证明[J]. 数学季刊, 2009, 24(1) |
| |
| 作者姓名： | 王建飞 刘太顺 |
| |
| 作者单位： | |
| |
| 基金项目： | 国家自然科学基金，浙江省自然科学基金 |
| |
| 摘 要： |
|
| 关 键 词： | 下界 证明 定理 失真 算子 单位球 星象函数 z1 |
A Simple Proof of the Lower Bounds of Distortion Theorems on the Roper-Suffridge Operator |
| |
| WANG Jian-fei LIU Tai-shun. A Simple Proof of the Lower Bounds of Distortion Theorems on the Roper-Suffridge Operator[J]. Chinese Quarterly Journal of Mathematics, 2009, 24(1) |
| |
| Authors: | WANG Jian-fei LIU Tai-shun |
| |
| Affiliation: | [1]Department of Mathematics and Physics, Zhejiang Normal University, Jinhua 321004, China [2]Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China |
| |
| Abstract: | Liczberski-Starkov first found a lower bound for ||D(f)|| near the origin, where is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again. |
| |
| Keywords: | distortion theorem convex mapping Roper-Suffridge operator |
| 本文献已被 维普 万方数据 等数据库收录！ |
