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A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS
JIANG, YUE-PING,RASILA, ANTTI,SUN, YONG Korean Mathematical Society 2015 대한수학회보 Vol.52 No.6
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].
A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS
Yue-Ping Jiang,Antti Rasila,Yong Sun 대한수학회 2015 대한수학회보 Vol.52 No.6
In this paper, we study right half-plane harmonic mappings f0 and f, where f0 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].