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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Published in:arXiv.org 2011-09
Main Authors: Ali, Rosihan M, Mahnaz, Moradi Nargesi, Ravichandran, V
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Language:English
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Analytic functions
Convexity
Inequalities
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description 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.
doi_str_mv 10.48550/arxiv.1109.0609
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subjects Analytic functions
Convexity
Inequalities
title Coefficient Inequalities for Starlikeness and Convexity
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