李书海,汤获,敖恩.由卷积和从属关系刻画的单叶调和函数某些子类[J].数学研究及应用,2019,39(1):31~42 |
由卷积和从属关系刻画的单叶调和函数某些子类 |
Certain Subclasses of Harmonic Univalent Functions Defined by Convolution and Subordination |
投稿时间:2018-01-16 修订日期:2018-08-12 |
DOI:10.3770/j.issn:2095-2651.2019.01.004 |
中文关键词: 单叶调和函数 从属 卷积 半径 |
英文关键词:Harmonic univalent functions subordination convolution radius |
基金项目:国家自然科学基金(Grant No.11561001),内蒙古高校青年科技英才支持计划资助项目(Grant No.NJYT-18-A14),内蒙古自然科学基金(Grant No.2014MS0101; 2018MS01026). |
|
摘要点击次数: 1320 |
全文下载次数: 1525 |
中文摘要: |
设$S_{H}$表示在单位圆盘$U=\{z:|z|<1\}$内局部单叶保向且满足$f(0)=f'_{z}(0)-1=0$的函数$f=h+\bar{g}$全体.本文引入了由卷积和从属关系定义$S_{H}$ 的某些新子类, 给出该类中函数的系数不等式, 偏差估计, 极值点和卷积性质. 此外, 还讨论了星象半径和凸半径问题. |
英文摘要: |
Let $S_{H}$ be the class of functions $f=h+\bar{g}$ that are harmonic univalent and sense-preserving in the open unit disk $\mathbb{U}=\{z\in \mathbb{C}:|z|<1\}$ for which $f(0)=f'(0)-1=0.$ In the present paper, we introduce some new subclasses of $S_{H}$ consisting of univalent and sense-preserving functions defined by convolution and subordination. Sufficient coefficient conditions, distortion bounds, extreme points and convolution properties for functions of these classes are obtained. Also, we discuss the radii of starlikeness and convexity. |
查看全文 查看/发表评论 下载PDF阅读器 |