On turán type inequalities for modified bessel functions

Arpád Baricz, Saminathan Ponnusamy

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31 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)523-532
Number of pages10
JournalProceedings of the American Mathematical Society
Volume141
Issue number2
DOIs
Publication statusPublished - Jan 1 2013

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Keywords

  • Completely monotonic functions
  • Modified Bessel functions
  • Turán-type inequalities

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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