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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Bohr inequality with a fixed zero coefficient
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by Seraj A. Alkhaleefah, Ilgiz R. Kayumov and Saminathan Ponnusamy PDF
Proc. Amer. Math. Soc. 147 (2019), 5263-5274 Request permission

Abstract:

In this paper, we introduce the study of the Bohr phenomenon for a quasisubordination family of functions, and establish the classical Bohr’s inequality for the class of quasisubordinate functions. As a consequence, we improve and obtain the exact version of the classical Bohr’s inequality for bounded analytic functions and also for $K$-quasiconformal harmonic mappings by replacing the constant term by the absolute value of the analytic part of the given function. We also obtain the Bohr radius for the subordination family of odd analytic functions.
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Additional Information
  • Seraj A. Alkhaleefah
  • Affiliation: Institute of Mathematics and Mechanics, Kazan Federal University, 420 008 Kazan, Russia
  • Email: s.alkhaleefah@gmail.com
  • Ilgiz R. Kayumov
  • Affiliation: Institute of Mathematics and Mechanics, Kazan Federal University, 420 008 Kazan, Russia
  • Email: ikayumov@gmail.com
  • Saminathan Ponnusamy
  • Affiliation: Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India
  • MR Author ID: 259376
  • ORCID: 0000-0002-3699-2713
  • Email: samy@iitm.ac.in
  • Received by editor(s): October 6, 2018
  • Received by editor(s) in revised form: March 22, 2019
  • Published electronically: July 30, 2019
  • Additional Notes: The research of the second author was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project 1.13556.2019/13.1. The work of the third author was supported by Mathematical Research Impact Centric Support of DST, India (MTR/2017/000367)
  • Communicated by: Stephan Ramon Garcia
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 5263-5274
  • MSC (2010): Primary 30A10, 30B10, 30C62, 30H05, 31A05, 41A58; Secondary 30C75, 40A30
  • DOI: https://doi.org/10.1090/proc/14634
  • MathSciNet review: 4021086