Coefficient Inequalities for Starlikeness and Convexity

Mathematics – Complex Variables

Scientific paper

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Scientific paper

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.

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