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Bohr Type Inequalities for the Class of Self-Analytic Maps on the Unit Disk

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Abstract

This article is devoted to sharp improvements of the classical Bohr inequality for the class \( \mathcal {B} \) of analytic self-maps defined on the unit disk \( \mathbb {D} \). In addition, we prove a sharp result which is an improved version of the classical Bohr inequality replacing the initial coefficients \( |a_0|, |a_1| \) and \( |a_2| \) in the majorant series by \( |f(z)|, |f^{\prime }(z)| \) and \( |f^{\prime \prime }(z)|/2! \) respectively.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

The authors are greatly indebted to the anonymous referees for their elaborate comments and valuable suggestions which improved significantly the presentation of the paper. The second author is supported by UGC-JRF (NTA Ref. No.: 201610135853), New Delhi, India.

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India

    Molla Basir Ahamed & Sabir Ahammed

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  1. Molla Basir Ahamed
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  2. Sabir Ahammed
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Correspondence to Molla Basir Ahamed.

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Communicated by Raymond Mortini.

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Ahamed, M.B., Ahammed, S. Bohr Type Inequalities for the Class of Self-Analytic Maps on the Unit Disk. Comput. Methods Funct. Theory 23, 789–806 (2023). https://doi.org/10.1007/s40315-023-00482-8

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