Extensions of Some Sufficient Conditions for Starlikeness and Convexity of Order $\beta$
Received:February 13, 2019  Revised:October 29, 2019
Key Word: Analytic functions   starlike function   convexity function   generalized Mitttag-Leffler function   generalized hypergeometric function
Fund ProjectL: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).
 Author Name Affiliation Xiaoyuan WANG School of Engineering and Management, Pingxiang University, Jiangxi 337055, P. R. China
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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.