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 - Funding Information:
We thank the anonymous referees for their very valuable comments and suggestions, which improved the previous version of the manuscript. The first author was supported by Universidad Nacional de Colombia, Hermes Code 49148. The second, third, and fifth authors were partially supported by Fondecyt, Chile Grants #1190756. The fourth author wishes to thank the Universidad del Cauca, Colombia for providing time for this work through research project VRI ID 5060.
Funding Information:
The second, third, and fifth authors were partially supported by Fondecyt, Chile Grants # 1190756 .
Funding Information:
The first author was supported by Universidad Nacional de Colombia , Hermes Code 49148 .
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 -