On the radius of starlikeness for harmonic mappings

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