| Initial Bounds for a Subclass of Analytic and Bi-Univalent Functions Defined by Chebyshev Polynomials and $q$-Differential Operator |
| Received:October 15, 2018 Revised:May 22, 2019 |
| Key Words:
analytic functions bi-univalent functions coefficient estimates Fekete-Szeg\"{o} inequality Chebyshev polynomials $q$-differential operator
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11561001; 11271045), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No.NJYT-18-A14), the Nature Science Foundation of Inner Mongolia of China (Grant No.2018MS01026), the Higher School Foundation of Inner Mongolia of China (Grant No.NJZY19211) and the Natural Science Foundation of Anhui Provincial Department of Education (Grant Nos.KJ2018A0833; KJ2018A0839), Provincial Quality Engineering Project of Anhui Colleges and Universities (Grant Nos.2018mooc608). |
| Author Name | Affiliation | | Dong GUO | Foundation Department, Chuzhou Vocational and Technical College, Anhui 239000, P. R. China | | En AO | 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 | | Liangpeng XIONG | School of Mathematics and Statistics, Wuhan University, Hubei 430072, P. R. China |
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| Abstract: |
| In this paper, we investigate the coefficient estimate and Fekete-Szeg\"{o} inequality of a subclass of analytic and bi-univalent functions defined by Chebyshev polynomials and $q$-differential operator. The results presented in this paper improve or generalize the recent works of other authors. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.05.007 |
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