On Starlike Meromorphic Functions of Order $\alpha$

Abstract:

      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.