Bull. Korean Math. Soc. 2015; 52(6): 1925-1935
Printed November 30, 2015
https://doi.org/10.4134/BKMS.2015.52.6.1925
Copyright © The Korean Mathematical Society.
Yue-Ping Jiang, Antti Rasila, and Yong Sun
Hunan University, Aalto University, Hunan University
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
2022; 59(4): 993-1010
2012; 49(4): 775-785
1998; 35(1): 99-117
2002; 39(1): 122-131
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd