Radius of convexity of partial sums of odd functions in the close-to-convex family

Abstract

∑ We consider the class of all analytic and locally univalent functions f of the form f (z) = z +∞n=2 a2n−1 z2n−1, |z| < 1, satisfying the condition (formula Presented) We show that every section (Formula Presented), of f, is convex in the disk |z| < 2/3. We also prove that the radius 2/3 is best possible, i.e. the number 2/3 cannot be replaced by a larger one. © 2017, University of Nis. All rights reserved.