ON CONVEX COMBINATIONS of CONVEX HARMONIC MAPPINGS

Álvaro Ferrada-Salas, Rodrigo Hernández, María J. Martín

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The family Fλ of orientation-preserving harmonic functions f = h+g in the unit disc (normalised in the standard way) satisfying {equation presented} for some {equation presented} , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in Fλ are convex.

Original languageEnglish
Pages (from-to)256-262
Number of pages7
JournalBulletin of the Australian Mathematical Society
Volume96
Issue number2
DOIs
StatePublished - 1 Oct 2017

Keywords

  • convex combinations
  • convex harmonic mappings

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