| Fekete-Szeg\"{o} Problems for Certain Classes of Meromorphic Functions Using $q$-Derivative Operator |
| Received:April 26, 2017 Revised:March 23, 2018 |
| Key Words:
analytic function meromorphic function Fekete-Szeg\"{o} problem $q$-derivative operator $q$-Bessel function
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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 Natural Science Foundation of Inner Mongolia (Grant Nos.\,2010MS0117; 2014MS0101; 2017MS0113), the Higher School Foundation of Inner Mongolia (Grant Nos.\,NJZY16251; NJZY17300; NJZY17301; NJZY18217) and the Natural Science Foundation of Chifeng. |
| Author Name | Affiliation | | Huo TANG | School of Mathematics and Statistics, Chifeng University, Inner Mongolia $024000$, P. R. China | | H. M. ZAYED | Department of Mathematics, Faculty of Science, Menofia University, Shebin Elkom 32511, Egypt | | A. O. MOSTAFA | Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt | | M. K. AOUF | Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt |
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| Abstract: |
| In this paper, we introduce two subclasses $\Sigma _{q}^{\ast }(\varphi )$ and\ $\Sigma _{q,\alpha }^{\ast }(\varphi )$ of meromorphic functions $f(z)$ for which $\frac{qzD_{q}f(z)}{f(z)}\prec \varphi (z)$ and $$\frac{-(1-\frac{\alpha }{q})qzD_{q}f(z)+\alpha qzD_{q}[zD_{q}f(z)] }{(1-\frac{\alpha }{q})f(z)-\alpha zD_{q}f(z)}\prec \varphi (z),\ \ \alpha \in \mathbb{C}\backslash (0,1],\ 0 |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.03.002 |
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