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AN APPLICATION OF SCHUR’S ALGORITHM TO VARIABILITY REGIONS OF CERTAIN ANALYTIC FUNCTIONS II
Part of:
Geometric function theory
Published online by Cambridge University Press: 02 December 2021
Abstract
We extend our study of variability regions, Ali et al. [‘An application of Schur algorithm to variability regions of certain analytic functions–I’, Comput. Methods Funct. Theory, to appear] from convex domains to starlike domains. Let 
$\mathcal {CV}(\Omega )$ be the class of analytic functions f in 
${\mathbb D}$ with 
$f(0)=f'(0)-1=0$ satisfying 
$1+zf''(z)/f'(z) \in {\Omega }$. As an application of the main result, we determine the variability region of 
$\log f'(z_0)$ when f ranges over 
$\mathcal {CV}(\Omega )$. By choosing a particular 
$\Omega $, we obtain the precise variability regions of 
$\log f'(z_0)$ for some well-known subclasses of analytic and univalent functions.
Keywords
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
The second author thanks SERB-MATRICS for financial support.
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