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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)
  • Received : 2014.08.19
  • Published : 2015.11.30

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

References

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Cited by

  1. Univalency of Convolutions of Univalent Harmonic Right Half-Plane Mappings vol.17, pp.2, 2017, https://doi.org/10.1007/s40315-016-0180-0