The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $alpha$-spirallike Functions
Journal: Sahand Communications in Mathematical Analysis (Vol.12, No. 1)Publication Date: 2018-11-01
Authors : Zahra Orouji; Rasul Aghalary;
Page : 89-96
Keywords : Pre-Schwarzian derivative; Spiral-like function; Uniformly convex function;
Abstract
For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$, we define
a subclass of the spirallike functions, $SP_{p}(alpha)$, the set
of all functions $fin mathcal{A}$
[
releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.
]
In the present paper, we shall give the estimate of the
norm of the pre-Schwarzian derivative $mathrm{T}_f=f''/f'$ where $|mathrm{T}_f|=sup_{zin Delta} (1-|z|^2)|mathrm{T}_f(z)|$ for the functions in $SP_{p}(alpha)$.
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Last modified: 2019-04-28 14:10:01