On the Analytic Part of Univalent Harmonic Mappings

摘要

In this article we obtain two sharp results concerning the analytic part of harmonic mappings from the class which was recently introduced by Ponnusamy and Sairam Kaliraj. For example, we get the sharp estimate for in the case when and obtain the sharp radius of convexity for h. Our approach is applicable to a more general situation. Finally, we determine simple condition on the analytic part of univalent harmonic mappings so that it is in spaces for 1/3.