Radius Constants for Analytic Functions with Fixed Second Coefficient

Let \(f(z)=z+\sum_{n=2}^{\infty}a_nz^n\) be analytic in the unit disk with second coefficient \(a_2\) satisfying \(|a_2|=2b\), \(0\leq b\leq1\). Sharp radius of Janowski starlikeness and other radius constants are obtained when \(|a_n|\leq cn+d\) (\(c,d\geq0\)) or \(|a_n|\leq c/n\) (\(c>0\)) for...

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Bibliographic Details
Published in:arXiv.org 2012-07
Main Authors: Ali, Rosihan M, Mahnaz, Moradi Nargesi, Ravichandran, V
Format: Article
Language:English
Subjects:
Analytic functions
Mathematical analysis
Online Access:Get full text
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Summary:Let \(f(z)=z+\sum_{n=2}^{\infty}a_nz^n\) be analytic in the unit disk with second coefficient \(a_2\) satisfying \(|a_2|=2b\), \(0\leq b\leq1\). Sharp radius of Janowski starlikeness and other radius constants are obtained when \(|a_n|\leq cn+d\) (\(c,d\geq0\)) or \(|a_n|\leq c/n\) (\(c>0\)) for \(n\geq3\).
ISSN:2331-8422