On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings

Abstract

In this paper, we give a negative answer to a problem presented by Bharanedhar and Ponnusamy 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-to-convex harmonic mappings, motivated by the work of Ponnusamy and Sairam Kaliraj, are obtained.