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

Abstract

For $0\le \alpha <1$, the sharp radii of starlikeness and convexity of order $\alpha$ for functions of the form $f(z)=z+a_2{z}^2+a_3{z}^3+...$ whose Taylor coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\le b\le 1$, and $|a_n|\le n$, $M$ or $M/n$ ($M>0$) for $n\ge 3$ are obtained. Also a class of functions related to Carathéodory functions is considered.

References in corpus (2)

• Uniformly Convex and Uniformly Starlike Functions
• Radius of Close-to-convexity of Harmonic Functions