On starlikeness and convexity of certain analytic functions

V. V. Anh and P. D. Tuan

Vol. 69 (1977), No. 1, 1–9

DOI: 10.2140/pjm.1977.69.1

Abstract

Let N be the class of normalised regular functions

For 0 ≦ λ < 1, γ ≧ 1, let f(z),g(z) ∈ N be such that

We establish the radius of starlikeness of f(z) under the assumption Re {g(z)∕z} > 0, or Re {g(z)∕z} > 1∕2, or Re {zg′(z)∕g(z)} > α, 0 ≦ α < 1, or Re {1 + zg′′(z)∕g′(z)} > 0 for |z| < 1. The analysis may be extended to the problem of finding the radius of convexity for certain subclasses of N.

Mathematical Subject Classification

Primary: 30A32, 30A32

Milestones

Received: 15 October 1976

Published: 1 March 1977