Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.

Abstract

For a constant $\alpha\in \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$,  we define
a  subclass of the spirallike functions, $SP_{p}(\alpha)$, the set
of all functions $f\in \mathcal{A}$
$\re\left\{e^{-i\alpha}\frac{zf'(z)}{f(z)}\right\}\geq\left|\frac{zf'(z)}{f(z)}-1\right|.$
In  the present paper, we shall give the estimate of the
norm of the pre-Schwarzian derivative  $\mathrm{T}_f=f''/f'$ where $\|\mathrm{T}_f\|=\sup_{z\in \Delta} (1-|z|^2)|\mathrm{T}_f(z)|$ for the functions in  $SP_{p}(\alpha)$.

Keywords

Main Subjects

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