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 -