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Refined Bohr-type inequalities with area measure for bounded analytic functions

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Abstract

In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the functions involved and thereby, we generalize several related results of earlier authors.

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Acknowledgements

This research of the first two authors are partly supported by Guangdong Natural Science Foundations (Grant No. 2018A030313508). The work of the third author was supported by Mathematical Research Impact Centric Support (MATRICS) of the Department of Science and Technology (DST), India (MTR/2017/000367). The authors of this paper thank the referees very much for their valuable comments and suggestions to this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, China

    Yong Huang & Ming-Sheng Liu

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

    Saminathan Ponnusamy

Authors
  1. Yong Huang
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  2. Ming-Sheng Liu
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  3. Saminathan Ponnusamy
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Correspondence to Ming-Sheng Liu.

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Huang, Y., Liu, MS. & Ponnusamy, S. Refined Bohr-type inequalities with area measure for bounded analytic functions. Anal.Math.Phys. 10, 50 (2020). https://doi.org/10.1007/s13324-020-00393-0

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