Radii of starlikeness and convexity of analytic functions satisfying certain coefficient inequalities

Abstract

For 0 ≤ α < 1, the sharp radii of starlikeness and convexity of order α for functions of the form f(z) = z + a2 z 2 + a3 z 3 + ... whose Taylor coefficients an satisfy the conditions {pipe}a2{pipe} = 2b, 0 ≤ b ≤ 1, and {pipe}an{pipe} ≤ n, M or M/n (M > 0) for n ≥ 3 are obtained. Also a class of functions related to Carathéodory functions is considered. © 2014 Versita Warsaw and Springer-Verlag Wien.