Certain Subclass of Meromorphic β-starlike Functions Associated with a Differential Operator
Abstract
Sharp bounds for the Fekete-Szegö functional $\left|v_1-\xi v_0{ }^2\right|$ are derived for certain class of meromorphic starlike functions $\omega(z)$ of order $\beta$ defined on the punctured open unit disk for which
$$
1-\frac{1}{t}\left(\frac{D^{n+1_{\circ} m} \omega(z)}{D^{n_0 m} \omega(z)}-1\right) \prec \chi(z) \quad\left(t \in \mathbb{C}-\{0\}, \eta \geq 0, \kappa>0, n, m \in \mathbb{N}_0\right)
$$
lie in a region starlike with respect to 1 and symmetric with respect to the real axis.
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