Radii of Starlikeness and Convexity of Analytic Functions Satisfying Certain Coefficient Inequalities

Details Radii of Starlikeness and Convexity of Analytic Functions Satisfying Certain Coefficient Inequalities Radii of Starlikeness and Convexity of Analytic Functions Satisfying Certain Coefficient Inequalities

2011-08-27

arxiv.org/abs/1108.5412v1

Mathematics

Complex Variables

Scientific paper

For $0\leq \alpha <1$, the sharp radii of starlikeness and convexity of order
$\alpha$ for functions of the form $f(z)=z+a_2z^2+a_3z^3+...$ whose Taylor
coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\leq b\leq 1$, and
$|a_n|\leq n $, $M$ or $M/n$ ($M>0$) for $n\geq 3$ are obtained. Also a class
of functions related to Carath\'eodory functions is considered.

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