TY - JOUR

T1 - A new approach for the univalence of certain integral of harmonic mappings

AU - Arbeláez, Hugo

AU - Bravo, Victor

AU - Hernández, Rodrigo

AU - Sierra, Willy

AU - Venegas, Osvaldo

N1 - Publisher Copyright:
© 2020 Royal Dutch Mathematical Society (KWG)

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

UR - http://www.scopus.com/inward/record.url?scp=85083658557&partnerID=8YFLogxK

U2 - 10.1016/j.indag.2020.04.002

DO - 10.1016/j.indag.2020.04.002

M3 - Article

AN - SCOPUS:85083658557

SN - 0019-3577

VL - 31

SP - 525

EP - 535

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 4

ER -