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 Re Pf (z) < 3 / 2 (Re Pf (z) > - 1 / 2 respectively) in | z | < 1, where Pf (z) = 1 + z f″ (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) = 3 λ}, respectively. © 2006 Elsevier Inc. All rights reserved.