A convolution property of univalent harmonic right half-plane mappings

Abstract

We consider the convolution of right half-plane harmonic mappings in the unit disk D:={z?C:|z|<1} with respective dilatations ei?(z+ a) / (1 + az) and - z, where - 1 < a< 1 and ?? R. We prove that such convolutions are locally univalent and convex in the horizontal direction under certain condition. � 2020, Springer-Verlag GmbH Austria, part of Springer Nature.