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Positivity

, Volume 22, Issue 5, pp 1403–1417 | Cite as

A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions

  • Jamel El Kamel
  • Khaled Mehrez
Article

Abstract

In this paper, we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite. We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions of the second kind. As applications, we prove the logarithmically monotonicity for a class of functions involving the modified Bessel functions of second kind and we established new inequalities for this function.

Keywords

Bessel functions Positive definite functions Completely monotonic functions Logarithmically completely monotonic functions 

Mathematics Subject Classification

42A82 33C10 26D07 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Département de MathématiquesFSMMonastirTunisia
  2. 2.Département de Mathématiques, Faculté de Sciences de TunisUniversité Tunis El ManarTunisTunisia
  3. 3.Département de Mathématiques ISSAT KasserineUniversité de KairouanKairouanTunisia

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