Radii Properties for Subclasses of Convex Functions

A function ƒ(z) = z + • • • is said to be in D if Re ƒ′(z) ≥ |zƒ′′ (z)|, |z| < 1. Using extreme point theory, the authors determine the largest disks |z| ≤ β = β(α) for which ƒ(βz)/β ∈ D when ƒ is convex of order α or when Re ƒ′(z) > α, 0 ≤ α < 1.