Extensions of some sufficient conditions for starlikeness and convexity of order $\beta$
Received:February 13, 2019  Revised:October 20, 2019
Key Word: Analytic functions   starlike function   convexity function   generalized Mitttag-Leffler function   generalized hypergeometric function.
Fund ProjectL:Youth Science Fund Research Project of Pingxiang University Grant no.2018D0218 and no.2018D0208
 Author Name Affiliation E-mail Xiaoyuan Wang Pingxiang University mewangxiaoyuan@163.com
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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.