On the Shears of Univalent Harmonic Mappings

M. Aydogan; D. Bshouty; A. Lyzzaik; F. M. Sakar

doi:10.1007/s11785-018-0855-9

On the Shears of Univalent Harmonic Mappings

M. Aydogan, D. Bshouty^*, A. Lyzzaik, F. M. Sakar

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let S be the standard class of normalized, univalent, analytic functions of the open unit disc D, and let SH0 be the class of sense-preserving, univalent, harmonic mappings f= h+ g¯ of D, where h(z)=z+∑n=2∞anznandg(z)=∑n=2∞bnzn.The purpose of this article is to disprove a conjecture by S. Ponnusamy and A. Sairam Kaliraj asserting that for every function f=h+g¯∈SH0, there exists a value θ∈ R such that the function h+ eⁱ ^θg∈ S.

Original language	English
Pages (from-to)	2853-2862
Number of pages	10
Journal	Complex Analysis and Operator Theory
Volume	13
Issue number	6
DOIs	https://doi.org/10.1007/s11785-018-0855-9
Publication status	Published - 1 Sept 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

Keywords

Convex domains in a direction
Harmonic mappings

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AU - Aydogan, M.

AU - Bshouty, D.

AU - Lyzzaik, A.

AU - Sakar, F. M.

PY - 2019/9/1

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N2 - Let S be the standard class of normalized, univalent, analytic functions of the open unit disc D, and let SH0 be the class of sense-preserving, univalent, harmonic mappings f= h+ g¯ of D, where h(z)=z+∑n=2∞anznandg(z)=∑n=2∞bnzn.The purpose of this article is to disprove a conjecture by S. Ponnusamy and A. Sairam Kaliraj asserting that for every function f=h+g¯∈SH0, there exists a value θ∈ R such that the function h+ ei θg∈ S.

AB - Let S be the standard class of normalized, univalent, analytic functions of the open unit disc D, and let SH0 be the class of sense-preserving, univalent, harmonic mappings f= h+ g¯ of D, where h(z)=z+∑n=2∞anznandg(z)=∑n=2∞bnzn.The purpose of this article is to disprove a conjecture by S. Ponnusamy and A. Sairam Kaliraj asserting that for every function f=h+g¯∈SH0, there exists a value θ∈ R such that the function h+ ei θg∈ S.

KW - Convex domains in a direction

KW - Harmonic mappings

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EP - 2862

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 6

ER -

On the Shears of Univalent Harmonic Mappings

Abstract

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Keywords

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