TY - JOUR ID - 31361 TI - The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $\alpha$-spirallike Functions JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Orouji, Zahra AU - Aghalary, Rasul AD - Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. Y1 - 2018 PY - 2018 VL - 12 IS - 1 SP - 89 EP - 96 KW - Pre-Schwarzian derivative KW - Spiral-like function KW - Uniformly convex function DO - 10.22130/scma.2018.68371.262 N2 - For a constant $\alpha\in \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$,  we definea  subclass of the spirallike functions, $SP_{p}(\alpha)$, the setof 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  $SP_{p}(\alpha)$. UR - https://scma.maragheh.ac.ir/article_31361.html L1 - https://scma.maragheh.ac.ir/article_31361_c141090df86a41f99564a5e04602b904.pdf ER -