$\alpha$阶星象亚纯函数

On Starlike Meromorphic Functions of Order $\alpha$

中文关键词:  亚纯函数  星象函数  泰勒系数  洛朗系数

英文关键词:meromorphic function  starlike function  Taylor coefficient  Laurent coefficient

中文摘要:

      令$S(p)$表示单位圆盘$\mathbb{D}$上在$p\in(0,1)$处有一个简单极点的单叶亚纯函数全体.令$\alpha\in[0,1)$,我们用$\Sigma^{*}(p,\omega_{0},\alpha)$表示$f\in S(p)$使得$\hat{\mathbb{C}}\setminus f(\mathbb{D})$是关于不动点$\omega_{0}\neq0$, $\infty$星象的$\alphga$阶区域的函数全体.在本文中,$f\in\Sigma^{*}(p,\omega_{0},\alpha)$的一些解析刻画条件和系数估计被考虑.

英文摘要:

      Let $S(p)$ be the class of all univalent meromorphic functions $f$ on the unit disk $\mathbb{D}$ with a simple pole at $p\in(0,1)$. For $\alpha\in[0,1),$ we denote by $\Sigma^{*}(p,\omega_{0},\alpha)$ the class of $f\in S(p)$ such that $\hat{\mathbb{C}}\setminus f(\mathbb{D})$ is a starlike domain of order $\alpha$ with respect to fixed point $\omega_{0}\neq0, \infty$. In this paper, some analytic characterizations and coefficient estimates of $f\in\Sigma^{*}(p,\omega_{0},\alpha)$ are considered.