Convexity theorems for subclasses of univalent functions

Herbert Silverman

Vol. 64 (1976), No. 1, 253–263

DOI: 10.2140/pjm.1976.64.253

Abstract

We determine the radius of convexity of functions f(z) for which Re{f′(z)∕ϕ′(z)} > β, where ϕ(z) is convex of order α(0 ≦ α ≦ 1). We also find bounds for |arg f′(z)|. All result are sharp.

Mathematical Subject Classification

Primary: 30A32, 30A32

Milestones

Received: 12 September 1975

Published: 1 May 1976