On Koebe radius and coefficients estimate for univalent harmonic mappings

Abstract: The problem on estimate of the Koebe radius for univalent harmonic mappings of the unit disk $\mathbb D={z\in\mathbb C : |z|<1}$ is considered. For a subclass of harmonic mappings with the standard normalization and a certain growth estimate for analytic dilatation, we provide new estimate for the Koebe radius. New estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary.