$\beta$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 $\beta$

中文关键词:  解析函数  星象函数  凸象函数  广义Mittag-Leffler函数  广义超几何函数

英文关键词:Analytic functions  starlike function  convexity function  generalized Mitttag-Leffler function  generalized hypergeometric function

中文摘要:

      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.

英文摘要:

      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.