Certain Subclasses of Harmonic Univalent Functions Defined by Convolution and Subordination

DOI：10.3770/j.issn:2095-2651.2019.01.004

 作者 单位 李书海 赤峰学院数学与统计学院, 内蒙古 赤峰 024000 汤获 赤峰学院数学与统计学院, 内蒙古 赤峰 024000 敖恩 赤峰学院数学与统计学院, 内蒙古 赤峰 024000

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.

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.