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http://dx.doi.org/10.4134/BKMS.2015.52.6.1925

A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS  

JIANG, YUE-PING (School of Mathematics and Econometrics Hunan University)
RASILA, ANTTI (Department of Mathematics and Systems Analysis Aalto University)
SUN, YONG (School of Mathematics and Econometrics Hunan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.6, 2015 , pp. 1925-1935 More about this Journal
Abstract
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].
Keywords
harmonic univalent mapping; convolution; half-plane mapping; convex function;
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Times Cited By KSCI : 1  (Citation Analysis)
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