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On Turán type inequalities for modified Bessel functions


Authors: Árpád Baricz and Saminathan Ponnusamy
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
Published electronically: June 4, 2012
MathSciNet review: 2996956
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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
Email: bariczocsi@yahoo.com

Saminathan Ponnusamy
Affiliation: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
Email: samy@iitm.ac.in

DOI: https://doi.org/10.1090/S0002-9939-2012-11325-5
Keywords: Modified Bessel functions, Turán-type inequalities, completely monotonic functions
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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