On a problem of bharanedhar and ponnusamy involving planar harmonic mappings

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

doi:10.1216/RMJ-2018-48-4-1345

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 journal › Article › peer-review

5 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 language	English
Pages (from-to)	1345-1358
Number of pages	14
Journal	Rocky Mountain Journal of Mathematics
Volume	48
Issue number	4
DOIs	https://doi.org/10.1216/RMJ-2018-48-4-1345
State	Published - 2018
Externally published	Yes

Keywords

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

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10.1216/RMJ-2018-48-4-1345

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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.",

keywords = "Close-to-convex harmonic mapping, Planar harmonic mapping, Univalent harmonic mapping",

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AU - Sun, Yong

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Y1 - 2018

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AB - 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.

KW - Close-to-convex harmonic mapping

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KW - Univalent harmonic mapping

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JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

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ER -

On a problem of bharanedhar and ponnusamy involving planar harmonic mappings

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Keywords

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