A new approach for the univalence of certain integral of harmonic mappings

Hugo Arbeláez; Victor Bravo; Rodrigo Hernández; Willy Sierra; Osvaldo Venegas

doi:10.1016/j.indag.2020.04.002

A new approach for the univalence of certain integral of harmonic mappings

Hugo Arbeláez, Victor Bravo, Rodrigo Hernández, Willy Sierra, Osvaldo Venegas

Faculty of Engineering and Science

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

5 Scopus citations

Abstract

The principal goal of this paper is to extend the classical problem of finding the values of α∈ℂ for which either fˆ_α(z)=∫₀^z(f(ζ)∕ζ)^αdζ or f_α(z)=∫₀^z(f^′(ζ))^αdζ are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4].

Original language	English
Pages (from-to)	525-535
Number of pages	11
Journal	Indagationes Mathematicae
Volume	31
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2020.04.002
State	Published - Jul 2020

Keywords

Geometric function theory
Integral transformation
Univalent mappings

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abstract = "The principal goal of this paper is to extend the classical problem of finding the values of α∈ℂ for which either fˆα(z)=∫0z(f(ζ)∕ζ)αdζ or fα(z)=∫0z(f′(ζ))αdζ are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4].",

keywords = "Geometric function theory, Integral transformation, Univalent mappings",

author = "Hugo Arbel{\'a}ez and Victor Bravo and Rodrigo Hern{\'a}ndez and Willy Sierra and Osvaldo Venegas",

note = "Publisher Copyright: {\textcopyright} 2020 Royal Dutch Mathematical Society (KWG)",

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AU - Arbeláez, Hugo

AU - Bravo, Victor

AU - Hernández, Rodrigo

AU - Sierra, Willy

AU - Venegas, Osvaldo

PY - 2020/7

Y1 - 2020/7

N2 - The principal goal of this paper is to extend the classical problem of finding the values of α∈ℂ for which either fˆα(z)=∫0z(f(ζ)∕ζ)αdζ or fα(z)=∫0z(f′(ζ))αdζ are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4].

AB - The principal goal of this paper is to extend the classical problem of finding the values of α∈ℂ for which either fˆα(z)=∫0z(f(ζ)∕ζ)αdζ or fα(z)=∫0z(f′(ζ))αdζ are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4].

KW - Geometric function theory

KW - Integral transformation

KW - Univalent mappings

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IS - 4

ER -

A new approach for the univalence of certain integral of harmonic mappings

Abstract

Keywords

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