A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS

作者:Jiang, Yue Ping*; Rasila, Antti; Sun, Yong
来源:Bulletin of the Korean Mathematical Society, 2015, 52(6): 1925-1935.
DOI:10.4134/BKMS.2015.52.6.1925

摘要

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 [11], which itself originates from a problem posed by Dorff et al. in [7].