A note on convexity of convolutions of harmonic mappings

Yue Ping Jiang, Antti Rasila, Yong Sun

Research output: Contribution to journalArticlepeer-review

6 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 languageEnglish
Pages (from-to)1925-1935
Number of pages11
JournalBulletin of the Korean Mathematical Society
Volume52
Issue number6
DOIs
StatePublished - 2015
Externally publishedYes

Keywords

  • Convex function
  • Convolution
  • Half-plane mapping
  • Harmonic univalent mapping

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