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A Generalization of the Bohr–Rogosinski Sum

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Abstract

In this paper, we investigate the classical Bohr sum for analytic functions defined on the unit disk in a general setting. In addition, we discuss a generalization of the Bohr–Rogosinski sum for a class of analytic functions subordinate to the univalent functions in the unit disk. Several well-known results are observed from the consequences of our main results.

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ACKNOWLEDGMENTS

The authors acknowledge the careful reading of the manuscript and suggestions made by the referee. The authors would like to thank Professor S. Ponnusamy for many fruitful discussions on this topic.

Funding

The work of the first author is supported by CSIR, New Delhi (grant no: 09/1022(0034)/2017-EMR-I).

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Authors and Affiliations

  1. School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, An OCC of Homi Bhabha National Institute, 752050, Jatni, India

    S. Kumar

  2. Department of Mathematics, Indian Institute of Technology Indore, 453552, Indore, India

    S. K. Sahoo

Authors
  1. S. Kumar
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  2. S. K. Sahoo
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Correspondence to S. Kumar or S. K. Sahoo.

Additional information

(Submitted by A. M. Elizarov)

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Kumar, S., Sahoo, S.K. A Generalization of the Bohr–Rogosinski Sum. Lobachevskii J Math 43, 2176–2186 (2022). https://doi.org/10.1134/S1995080222110166

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  • DOI: https://doi.org/10.1134/S1995080222110166

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