$\beta$阶星象函数和凸象函数的几个充分条件的扩展
Extensions of Some Sufficient Conditions for Starlikeness and Convexity of Order $\beta$

DOI：10.3770/j.issn:2095-2651.2020.03.004

 作者 单位 王小元 萍乡学院工程与管理学院, 江西 萍乡 337055

本文目的是研究了两个新算子$\mathcal{E}_{\alpha, \lambda}^{\gamma}$和$H_{m}^{l}(\alpha_1)$的星形和凸性的几个充分条件, 分别与定义在单位圆盘的广义Mittag-Leffler函数$E_{\alpha, \lambda}^{\gamma}$和广义超几何函数有关.本文得出的结果与早期的一些已知结果建立联系.

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.