| Certain Subclasses of Harmonic Univalent Functions Defined by Convolution and Subordination |
| Received:January 16, 2018 Revised:August 12, 2018 |
| Key Words:
Harmonic univalent functions subordination convolution radius
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11561001), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No.NJYT-18-A14) and the Natural Science Foundation of Inner Mongolia Province (Grant Nos.2014MS0101; 2018MS01026). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.01.004 |
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