On the Radius of Starlikeness for Harmonic Mappings

Abstract

In this paper, we obtain a criterion of starlikeness for the image of the disk with center at the origin and radius r ∈ (0, 1) under a univalent harmonic mapping by a function that maps the unit disk onto a convex domain. This criterion is similar to the criterion of image convexity, and it is expressed in terms of starlikeness in one direction. As a corollary, we obtain a new estimate for the radius of starlikeness of the class of univalent harmonic mappings that take the unit disk onto a convex domain.