Estimates of Growth for Certain Convex and Close-to-Convex Functions in the Unit DISC

Abstract

Let S denote the class of all univalent analytic functions f defined in the unit disc and normalised by the conditions f(0) = 0,f'(0) = 1. For a fixed α, 0 < α < 1, let C(α) denote the sub-class of S, consisting of all functions f satisfying the differential inequality

Re {z f"/f'}+1>α for |z| <1.