Linear combinations of harmonic quasiconformal mappings convex in one direction

Yong Sun, Antti Rasila, Yue Ping Jiang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper, we introduce a new class (Formula presented) (k; γ; ɸ) of harmonic quasiconformal mappings, where k ∈ [0, 1), γ ∈ [0, π) and ɸ is an analytic function. Sufcient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of γ and ɸ, are convex.

Original languageEnglish
Pages (from-to)366-377
Number of pages12
JournalKodai Mathematical Journal
Volume39
Issue number2
DOIs
StatePublished - 2016
Externally publishedYes

Keywords

  • Convex in one direction
  • Harmonic K-quasiconformal mapping
  • Linear combination
  • Univalent harmonic mapping

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