Coefficient Bounds for a New Subclass of Bi-Univalent Functions Defined by Salagean Operator
Received:July 29, 2016  Revised:September 07, 2016
Key Words: analytic functions   univalent functions   bi-univalent functions   coefficient bounds   Salagean operator
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11401186) and the Research Fund from Engineering and Technology College Yangtze University (Grant No.15J0802).
 Author Name Affiliation Fan CHEN College of Engineering and Technology, Yangtze University, Hubei 434000, P. R. China Xiaofei LI School of Information and Mathematics, Yangtze University, Hubei $434000$, P. R. China Department of Mathematics, University of Macau, Macau 999078, P. R. China
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In this paper, a new subclass $\mathcal {N}^{h,p}_{\Sigma}(m,\lambda,\mu)$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$ is defined by salagean operator. We obtain coefficients bounds $|a_{2}|$ and $|a_{3}|$ for functions of the class. Moreover, we verify Brannan and Clunie's conjecture $|a_{2}|\leq\sqrt{2}$ for some of our classes. The results in this paper extend many results recently researched by many authors.