Convex combinations of harmonic shears of slit mappings

Lei Shi, Zhi Gang Wang, Antti Rasila*, Yong Sun

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings. Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived. Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate potential applications of the main results.

Original languageEnglish
Pages (from-to)1495-1510
Number of pages16
JournalBulletin of the Iranian Mathematical Society
Volume43
Issue number5
StatePublished - Oct 2017
Externally publishedYes

Keywords

  • Convex combination
  • Harmonic mapping
  • Shear construction
  • Slit mapping

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