Regions of variability for convex functions

Abstract

Abstract Let 𝒞 be the class of convex univalent functions f in the unit disc 𝔻 normalized by f (0) = f ′(0) – 1 = 0. For z 0 ∈ 𝔻 and | λ | ≤ 1 we shall determine explicitly the regions of variability {log f ′( z 0 ): f ∈ 𝒞, f ″(0) = 2 λ }. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)