Certain Subclasses of Harmonic Univalent Functions Defined by Convolution and Subordination
Received:January 16, 2018  Revised:August 12, 2018
Key Word: Harmonic univalent functions   subordination   convolution   radius
Fund ProjectL: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).
 Author Name Affiliation Shuhai LI School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China Huo TANG School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China En AO School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China
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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.