| Extensions of Some Sufficient Conditions for Starlikeness and Convexity of Order $\beta$ |
| Received:February 13, 2019 Revised:October 29, 2019 |
| Key Words:
Analytic functions starlike function convexity function generalized Mitttag-Leffler function generalized hypergeometric function
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| Fund Project:Supported by the Youth Science Fund Research Project of Pingxiang University (Grant Nos.2019D0202; 2018D0218; 2018D0208) and the Youth Fund Project of Science and Technology Research Project of Jiangxi Provincial Department of Education (Grant No.GJJ191157). |
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| Abstract: |
| The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operators $\mathcal{E}_{\alpha, \lambda}^{\gamma} $ and $H_{m}^{l}(\alpha_1)$ related to the generalized Mittag-Leffler function $E_{\alpha, \lambda}^{\gamma}$ and the generalized hypergeometric function, defined in the unit disk, respectively. The results presented here make connections to some of the earlier known developments. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2020.03.004 |
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