A1 Refereed original research article in a scientific journal
Functional inequalities for modified Bessel functions
Authors: Baricz A, Ponnusamy S, Vuorinen M
Publisher: ELSEVIER GMBH, URBAN & FISCHER VERLAG
Publication year: 2011
Journal: Expositiones Mathematicae
Journal name in source: Expositiones Mathematicae
Journal acronym: EXPO MATH
Number in series: 4
Volume: 29
Issue: 4
First page : 399
Last page: 414
Number of pages: 16
ISSN: 0723-0869
DOI: https://doi.org/10.1016/j.exmath.2011.07.001
Web address : http://api.elsevier.com/content/abstract/scopus_id:83055188286
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. © 2011 Elsevier Ltd.
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. © 2011 Elsevier Ltd.
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