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

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

6 Scopus citations

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.

Original language	English
Pages (from-to)	733-754
Number of pages	22
Journal	Monatshefte fur Mathematik
Volume	199
Issue number	4
DOIs	https://doi.org/10.1007/s00605-021-01659-w
State	Published - Dec 2022
Externally published	Yes

Keywords

Harmonic and logharmonic mappings
Pre-Schwarzian and Schwarzian derivatives
Univalence criterion

Access to Document

10.1007/s00605-021-01659-w

Cite this

@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 = "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.

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this