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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 456, 2017, pp. 16–24.
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Bagapsh, A.O. On the Radius of Starlikeness for Harmonic Mappings. J Math Sci 234, 276–281 (2018). https://doi.org/10.1007/s10958-018-4003-x
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DOI: https://doi.org/10.1007/s10958-018-4003-x