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Bohr Inequality for Odd Analytic Functions

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Abstract

We determine the Bohr radius for the class of odd functions f satisfying \(|f(z)|\le 1\) for all \(|z|<1\), solving the recent problem of Ali et al. (J Math Anal Appl 449(1):154–167, 2017). In fact, we solve this problem in a more general setting. Then we discuss Bohr’s radius for the class of analytic functions g, when g is subordinate to a member of the class of odd univalent functions.

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Acknowledgements

The research of the first author was supported by Russian foundation for basic research, Proj. 17-01-00282, and the research of the second author was supported by the project RUS/RFBR/P-163 under Department of Science & Technology (India). The second author is currently working at the ISI Chennai Centre.

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Authors and Affiliations

  1. Kazan Federal University, Kremlevskaya 18, Kazan, 420 008, Russia

    Ilgiz R Kayumov

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

    Saminathan Ponnusamy

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  1. Ilgiz R Kayumov
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  2. Saminathan Ponnusamy
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Correspondence to Saminathan Ponnusamy.

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Communicated by Dmitri Khavinson.

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Kayumov, I.R., Ponnusamy, S. Bohr Inequality for Odd Analytic Functions. Comput. Methods Funct. Theory 17, 679–688 (2017). https://doi.org/10.1007/s40315-017-0206-2

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  • DOI: https://doi.org/10.1007/s40315-017-0206-2

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