A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS

Title & Authors
A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS
JIANG, YUE-PING; RASILA, ANTTI; SUN, YONG;

Abstract
In this paper, we study right half-plane harmonic mappings $\small{f_0}$ and f, where $\small{f_0}$ 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].
Keywords
harmonic univalent mapping;convolution;half-plane mapping;convex function;
Language
English
Cited by
1.
Univalency of Convolutions of Univalent Harmonic Right Half-Plane Mappings, Computational Methods and Function Theory, 2017, 17, 2, 289
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