On harmonic typically real mappings

In this paper, we prove that a univalent orientation-preserving harmonic mapping f = h + ¯g defined on the unit disk U with the normalization f (0) = 0, h (0) + g (0) > 0, is a typically real mapping, if f (U) is a starlike domain with respect to the origin or f (U) is convex in one direction.  2003 Elsevier Science (USA). All rights reserved