| 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
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| 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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.03.006 |
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