A convolution property of univalent harmonic right half-plane mappings

Article Type

Research Article

Publication Title

Monatshefte fur Mathematik

Abstract

We consider the convolution of right half-plane harmonic mappings in the unit disk D:={z∈C:|z|<1} with respective dilatations eiα(z+ a) / (1 + az) and - z, where - 1 < a< 1 and α∈ R. We prove that such convolutions are locally univalent and convex in the horizontal direction under certain condition.

First Page

729

Last Page

736

DOI

10.1007/s00605-020-01442-3

Publication Date

12-1-2020

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