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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