Region of variability of two subclasses of univalent functions

Let F1 (F2 respectively) denote the class of analytic functions f in the unit disk |z| < 1 with f (0) = 0 = f (0) − 1 satisfying the condition RePf (z) < 3/2 (RePf (z) > −1/2 respectively) in |z| < 1, where Pf (z) = 1+zf (z)/f (z). For any fixed z0 in the unit disk and λ ∈ [0, 1), we shall determine the region of variability for log f (z0) when f ranges over the class {f ∈ F1: f (0)=−λ} and {f ∈ F2: f (0) = 3λ}, respectively. © 2006 Elsevier Inc. All rights reserved