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2018 On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings
Zhi-Gang Wang, Zhi-Hong Liu, Antti Rasila, Yong Sun
Rocky Mountain J. Math. 48(4): 1345-1358 (2018). DOI: 10.1216/RMJ-2018-48-4-1345

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.

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Zhi-Gang Wang. Zhi-Hong Liu. Antti Rasila. Yong Sun. "On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings." Rocky Mountain J. Math. 48 (4) 1345 - 1358, 2018. https://doi.org/10.1216/RMJ-2018-48-4-1345

Information

Published: 2018
First available in Project Euclid: 30 September 2018

zbMATH: 06958782
MathSciNet: MR3859761
Digital Object Identifier: 10.1216/RMJ-2018-48-4-1345

Subjects:
Primary: 30C55, 58E20

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 4 • 2018
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