On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings
Complex Variables
2017-08-23 v2
Abstract
In this paper, we give a negative answer to a problem presented by Bharanedhar and Ponnusamy (Rocky Mountain J. Math. 44: 753--777, 2014) 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, which is motivated by work of Ponnusamy and Sairam Kaliraj (Mediterr. J. Math. 12: 647--665, 2015), are obtained.
Cite
@article{arxiv.1703.09478,
title = {On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings},
author = {Zhi-Gang Wang and Zhi-Hong Liu and Antti Rasila and Yong Sun},
journal= {arXiv preprint arXiv:1703.09478},
year = {2017}
}
Comments
11 pages, 2 figures. To appear in Rocky Mountain J. Math