Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings

V. Bravo; R. Hernández; S. Ponnusamy; O. Venegas

doi:10.1007/s00605-021-01659-w

Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings

V. Bravo, R. Hernández, S. Ponnusamy, O. Venegas

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

2 Citas (Scopus)

Resumen

We introduce definitions of pre-Schwarzian and Schwarzian derivatives for logharmonic mappings, and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic.

Idioma original	Inglés
Páginas (desde-hasta)	733-754
Número de páginas	22
Publicación	Monatshefte fur Mathematik
Volumen	199
N.º	4
DOI	https://doi.org/10.1007/s00605-021-01659-w
Estado	Publicada - dic. 2022
Publicado de forma externa	Sí

Acceder al documento

10.1007/s00605-021-01659-w

Citar esto

@article{9173cc4b4da9473baeaf81a3ffbe1615,

title = "Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings",

abstract = "We introduce definitions of pre-Schwarzian and Schwarzian derivatives for logharmonic mappings, and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic.",

keywords = "Harmonic and logharmonic mappings, Pre-Schwarzian and Schwarzian derivatives, Univalence criterion",

author = "V. Bravo and R. Hern{\'a}ndez and S. Ponnusamy and O. Venegas",

note = "Funding Information: The authors were partially supported by Fondecyt Grants # 1190756. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.",

year = "2022",

month = dec,

doi = "10.1007/s00605-021-01659-w",

language = "English",

volume = "199",

pages = "733--754",

journal = "Monatshefte fur Mathematik",

issn = "0026-9255",

publisher = "Springer-Verlag Wien",

number = "4",

}

TY - JOUR

T1 - Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings

AU - Bravo, V.

AU - Hernández, R.

AU - Ponnusamy, S.

AU - Venegas, O.

N1 - Funding Information: The authors were partially supported by Fondecyt Grants # 1190756. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.

PY - 2022/12

Y1 - 2022/12

N2 - We introduce definitions of pre-Schwarzian and Schwarzian derivatives for logharmonic mappings, and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic.

AB - We introduce definitions of pre-Schwarzian and Schwarzian derivatives for logharmonic mappings, and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic.

KW - Harmonic and logharmonic mappings

KW - Pre-Schwarzian and Schwarzian derivatives

KW - Univalence criterion

UR - http://www.scopus.com/inward/record.url?scp=85123603148&partnerID=8YFLogxK

U2 - 10.1007/s00605-021-01659-w

DO - 10.1007/s00605-021-01659-w

M3 - Article

AN - SCOPUS:85123603148

SN - 0026-9255

VL - 199

SP - 733

EP - 754

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 4

ER -

Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings

Resumen

Acceder al documento

Huella

Citar esto