On a problem of bharanedhar and ponnusamy involving planar harmonic mappings

Zhi Gang Wang, Zhi Hong Liu, Antti Rasila, Yong Sun

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, we give a negative answer to a problem presented by Bharanedhar and Ponnusamy [1] concerning univalency of a class of harmonic mappings. More precisely, we show that for all values of the involved parameter, this class contains a non-univalent function. Moreover, several results on a new subclass of close-toconvex harmonic mappings, motivated by the work of Ponnusamy and Sairam Kaliraj [16], are obtained.

Original languageEnglish
Pages (from-to)1345-1358
Number of pages14
JournalRocky Mountain Journal of Mathematics
Volume48
Issue number4
DOIs
StatePublished - 2018

Keywords

  • Close-to-convex harmonic mapping
  • Planar harmonic mapping
  • Univalent harmonic mapping

Fingerprint Dive into the research topics of 'On a problem of bharanedhar and ponnusamy involving planar harmonic mappings'. Together they form a unique fingerprint.

Cite this