Pre-Schwarzian derivative for Logharmonic mapppings

V. Bravo; R. Hernandez; O. Venegas

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arXiv · 2006.07753

Pre-Schwarzian derivative for Logharmonic mapppings

V. Bravo·R. Hernandez·O. Venegas

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Abstract

We introduce a new definition of pre-Schwarzian derivative 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-Schwarzain is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic.

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V. Bravo, R. Hernandez, O. Venegas. 2020-06-14. Pre-Schwarzian derivative for Logharmonic mapppings. https://arxiv.org/abs/2006.07753

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