In this paper we study some properties of functions f which are analytic and normalized (i.e. \(f(0)=0=f'(0)-1\)) such that satisfy the following subordination relation

$$\begin{aligned} \left( \frac{zf'(z)}{f(z)}-1\right) \prec \frac{z}{(1-pz)(1-qz)}, \end{aligned}$$

where \((p,q) \in [-1,1] \times [-1,1]\). These types of functions are starlike related to the generalized Koebe function. Some of the features are: radius of starlikeness of order \(\gamma \in [0,1)\), image of \(f\left( \{z:|z|<r\}\right) \) where \(r\in (0,1)\), radius of convexity, estimation of initial and logarithmic coefficients, and Fekete–Szegö problem.

中文翻译：

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与广义 Koebe 函数相关的星状函数

在本文中，我们研究了解析和归一化的函数f 的一些性质（即\(f(0)=0=f'(0)-1\)）满足以下从属关系

$$\begin{aligned} \left( \frac{zf'(z)}{f(z)}-1\right) \prec \frac{z}{(1-pz)(1-qz)}, \end{对齐}$$

其中\((p,q) \in [-1,1] \times [-1,1]\)。这些类型的函数与广义 Koebe 函数呈星状相关。的一些功能是：为了星形性的半径\（\伽玛\在[0,1）\）的，图像\（F \左（\ {Z：| Z | <R \} \右）\） ，其中\(r\in (0,1)\)、凸面半径、初始和对数系数的估计以及 Fekete-Szegö 问题。