Coefficient Inequalities for Starlikeness and Convexity

For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on \(\beta\) is determined so that \(f\) is either starlike or convex of order \(\alpha\). Several other coefficient inequalities related to certain subclasses are...

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Bibliographic Details
Published in:arXiv.org 2011-09
Main Authors: Ali, Rosihan M, Mahnaz, Moradi Nargesi, Ravichandran, V
Format: Article
Language:English
Subjects:
Analytic functions
Convexity
Inequalities
Online Access:Get full text
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Summary:For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on \(\beta\) is determined so that \(f\) is either starlike or convex of order \(\alpha\). Several other coefficient inequalities related to certain subclasses are also investigated.
ISSN:2331-8422
DOI:10.48550/arxiv.1109.0609