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On the Pre-Schwarzian Norm of Certain Logharmonic Mappings

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Abstract

We connect the pre-Schwarzian norm of logharmonic mappings to the pre-Schwarzian norm of an analytic function and establish some necessary and sufficient conditions under which locally univalent logharmonic mappings have a finite pre-Schwarzian norm. We also obtain a necessary and sufficient condition for a logharmonic function to be Bloch. Furthermore, we obtain the pre-Schwarzian norm and growth theorem for logharmonic Bloch mappings and their analytic and co-analytic parts.

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Acknowledgements

The authors thank the referee for the constructive comments which helped to improve the presentation of the paper. The second named author thanks the Department Of Science and Technology, Ministry Of Science and Technology, Government Of India, for the financial support through DST-INSPIRE Fellowship (No. DST/INSPIRE Fellowship/2018/IF180967).

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Durgapur, West Bengal, 713209, India

    Md Firoz Ali & Sushil Pandit

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  1. Md Firoz Ali
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  2. Sushil Pandit
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All authors contributed equally to the investigation of the problem and the order of the authors is given alphabetically according to their surname. All authors read and approved the final manuscript.

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Correspondence to Md Firoz Ali.

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Communicated by See Keong Lee.

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Ali, M.F., Pandit, S. On the Pre-Schwarzian Norm of Certain Logharmonic Mappings. Bull. Malays. Math. Sci. Soc. 47, 67 (2024). https://doi.org/10.1007/s40840-024-01668-6

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  • DOI: https://doi.org/10.1007/s40840-024-01668-6

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