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arXiv · 2308.12505

On the pre-Schwarzian norm of certain Logharmonic mappings

Md Firoz Ali·Sushil Pandit
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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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Md Firoz Ali, Sushil Pandit. 2023-08-24. On the pre-Schwarzian norm of certain Logharmonic mappings. https://arxiv.org/abs/2308.12505

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