ResearchBib Share Your Research, Maximize Your Social Impacts
Sign for Notice Everyday Sign up >> Login

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:

Authors : ; ;

Page : 89-96

Keywords : Pre-Schwarzian derivative; Spiral-like function; Uniformly convex function;

Source : Download Find it from : Google Scholarexternal


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  $SP_{p}(alpha)$.

Last modified: 2019-04-28 14:10:01