A note on convexity of convolutions of harmonic mappings

Yue Ping Jiang; Antti Rasila; Yong Sun

doi:10.4134/BKMS.2015.52.6.1925

A note on convexity of convolutions of harmonic mappings

Yue Ping Jiang, Antti Rasila, Yong Sun

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8 Scopus citations

Abstract

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 Dorrff et al. in [7].

Original language	English
Pages (from-to)	1925-1935
Number of pages	11
Journal	Bulletin of the Korean Mathematical Society
Volume	52
Issue number	6
DOIs	https://doi.org/10.4134/BKMS.2015.52.6.1925
State	Published - 2015
Externally published	Yes

Keywords

Convex function
Convolution
Half-plane mapping
Harmonic univalent mapping

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10.4134/BKMS.2015.52.6.1925

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AU - Jiang, Yue Ping

AU - Rasila, Antti

AU - Sun, Yong

PY - 2015

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N2 - 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 Dorrff et al. in [7].

AB - 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 Dorrff et al. in [7].

KW - Convex function

KW - Convolution

KW - Half-plane mapping

KW - Harmonic univalent mapping

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ER -

A note on convexity of convolutions of harmonic mappings

Abstract

Keywords

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