Further Results for a Spirallike Functions of Order b
Let \Delta be the unit disk on the complex plane \mathbb{C} and \mathcal{A} be the class of normalized analytic functions in \Delta We denote by \mathcal{S}_{\alpha \beta the class of \alpha spirallike functions f of order \beta as follows \begin{aligned} \mathcal{S}_{\alpha \beta \left\ f\in \mathcal{A} \mathrm{Re}\left\ e^{i\alpha \frac{zf'(z){f(z)\right\ \beta \cos \alpha z\in \Delta \right\ \end{aligned} where \alpha \pi /2$ and \beta \in [0,1) In the present paper, some properties of this certain subclass of analytic functions including, subordination relations, estimates of logarithmic coefficients $f\in \mathcal{S}_{\alpha \beta coefficients inequality and Fekete Szego inequality for the kth root transform of $f\in \mathcal{S}_{\alpha \beta are investigated.