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

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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.

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Authors and Affiliations

  1. Département de Mathématiques, FSM, 5000, Monastir, Tunisia

    Jamel El Kamel

  2. Département de Mathématiques, Faculté de Sciences de Tunis, Université Tunis El Manar, Tunis, Tunisia

    Khaled Mehrez

  3. Département de Mathématiques ISSAT Kasserine, Université de Kairouan, Kairouan, Tunisia

    Khaled Mehrez

Authors
  1. Jamel El Kamel
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  2. Khaled Mehrez
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Correspondence to Khaled Mehrez.

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El Kamel, J., Mehrez, K. A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions. Positivity 22, 1403–1417 (2018). https://doi.org/10.1007/s11117-018-0584-3

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  • DOI: https://doi.org/10.1007/s11117-018-0584-3

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