Functional inequalities for modified Bessel functions

A. Baricz, Saminathan Ponnusamy, Matti Vuorinen

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper, our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kind. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Turán-type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind, we prove that the cumulative distribution function of the gamma-gamma distribution is log-concave. At the end of this paper, several open problems are posed, which may be of interest for further research.

Original languageEnglish
Pages (from-to)399-414
Number of pages16
JournalExpositiones Mathematicae
Volume29
Issue number4
DOIs
Publication statusPublished - 2011

Fingerprint

Neumann function
Modified Bessel Functions
Functional Inequalities
Bessel function of the first kind
Logarithmic Derivative
Log-concave
Cumulative distribution function
Gamma distribution
Mean Value
Open Problems

Keywords

  • Convexity with respect to Hölder means
  • Functional inequalities
  • Gamma-gamma distribution
  • Geometrical convexity
  • Log-convexity
  • Modified Bessel functions
  • Turán-type inequality

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Functional inequalities for modified Bessel functions. / Baricz, A.; Ponnusamy, Saminathan; Vuorinen, Matti.

In: Expositiones Mathematicae, Vol. 29, No. 4, 2011, p. 399-414.

Research output: Contribution to journalArticle

Baricz, A. ; Ponnusamy, Saminathan ; Vuorinen, Matti. / Functional inequalities for modified Bessel functions. In: Expositiones Mathematicae. 2011 ; Vol. 29, No. 4. pp. 399-414.
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