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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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 Turán type inequalities for modified Bessel functions
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by Árpád Baricz and Saminathan Ponnusamy PDF
Proc. Amer. Math. Soc. 141 (2013), 523-532 Request permission

Abstract:

In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Turán type inequalities for these functions. Moreover, we present some new Turán type inequalities for the aforementioned functions and we show that their product is decreasing as a function of the order, which has an application in the study of stability of radially symmetric solutions in a generalized FitzHugh-Nagumo equation in two spatial dimensions. At the end of this note an open problem is posed, which may be of interest for further research.
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Additional Information
  • Árpád Baricz
  • Affiliation: Department of Economics, Babeş-Bolyai University, Cluj-Napoca 400591, Romania
  • MR Author ID: 729952
  • Email: bariczocsi@yahoo.com
  • Saminathan Ponnusamy
  • Affiliation: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
  • MR Author ID: 259376
  • ORCID: 0000-0002-3699-2713
  • Email: samy@iitm.ac.in
  • Received by editor(s): April 23, 2010
  • Received by editor(s) in revised form: June 28, 2011
  • Published electronically: June 4, 2012
  • Communicated by: Sergei K. Suslov
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 523-532
  • MSC (2010): Primary 33C10, 39B62
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11325-5
  • MathSciNet review: 2996956