Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study right half-plane harmonic mappings $f_0$ and $f$, where $f_0$ is fixed and $f$ is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy \cite{lp1}, which itself originates from a problem posed by Dorff {\it et al.} in \cite{dor2012}.

Keywords: harmonic univalent mapping, convolution, half-plane mapping, convex function

MSC numbers: Primary 30C45; Secondary 30C20, 30C65