In the present investigation, a third order differential subordination result of Antonino and Miller (Complex Var Ellipt Equ 56(5):439–454, 2011) has been modified to accommodate Ma–Minda functions so that new avenues could be explored related to them. Further as an application, many alluring results pertaining to $${\mathscr {S}}^*_{SG}=\{f\in {\mathscr {A}}:zf'(z)/f(z)\prec 2/(1+e^{-z})\}$$ , the class of Sigmoid starlike functions, involving higher order differential subordinations are also obtained.

中文翻译：

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星状函数和高阶微分从属

在本研究中，Antonino 和 Miller（Complex Var Ellipt Equ 56(5):439–454, 2011）的三阶微分从属结果已被修改以适应 Ma-Minda 函数，以便可以探索与它们相关的新途径. 进一步作为应用程序，许多与 $${\mathscr {S}}^*_{SG}=\{f\in {\mathscr {A}}:zf'(z)/f(z)\ 有关的诱人结果prec 2/(1+e^{-z})\}$$ ，Sigmoid 类星形函数，涉及高阶微分从属也得到。