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Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings

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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.

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Data Availability Statement

The authors declare that this research is purely theoretical and does not associate with any data.

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Authors and Affiliations

  1. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar, Chile

    V. Bravo & R. Hernández

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    S. Ponnusamy

  3. Department of Mathematics, Petrozavodsk State University, ul., Lenina 33, Petrozavodsk, Russia, 185910

    S. Ponnusamy

  4. Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Av. Rudecindo Ortega 02950, Temuco, Chile

    O. Venegas

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  1. V. Bravo
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  2. R. Hernández
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  3. S. Ponnusamy
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  4. O. Venegas
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Correspondence to S. Ponnusamy.

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Communicated by Adrian Constantin.

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The authors were partially supported by Fondecyt Grants # 1190756.

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Bravo, V., Hernández, R., Ponnusamy, S. et al. Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings. Monatsh Math 199, 733–754 (2022). https://doi.org/10.1007/s00605-021-01659-w

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  • DOI: https://doi.org/10.1007/s00605-021-01659-w

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