On Starlike Meromorphic Functions of Order $\alpha$
Received:May 04, 2021  Revised:February 18, 2022
Key Word: meromorphic function   starlike function   Taylor coefficient   Laurent coefficient
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11871215).
 Author Name Affiliation Lei LIU Department of Mathematics, Nanjing University of Science and Technology, Jiangsu 210094, P. R. China Jinhua FAN Department of Mathematics, Nanjing University of Science and Technology, Jiangsu 210094, P. R. China
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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.