SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND

Title & Authors
SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND
Guo, Bai-Ni; Qi, Feng;

Abstract
By employing a refined version of the $\small{P{\acute{o}}lya}$ type integral inequality and other techniques, the authors establish some inequalities and absolute monotonicity for modified Bessel functions of the first kind with nonnegative integer order.
Keywords
inequality;absolute monotonicity;complete monotonic function;modified Bessel function of the first kind;$\small{P{\acute{o}}lya}$ type integral inequality;
Language
English
Cited by
1.
A double inequality for an integral mean in terms of the exponential and logarithmic means, Periodica Mathematica Hungarica, 2016
References
1.
M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, 10th printing, Dover Publications, New York and Washington, 1972.

2.
R. P. Agarwal and S. S. Dragomir, An application of Hayashi inequality for differentiable functions, Comput. Math. Appl. 32 (1996), no. 6, 95-99.

3.
A. Baricz, Bounds for modified Bessel functions of the first and second kinds, Proc. Edinb. Math. Soc. 53 (2010), no. 3, 575-599.

4.
A. Baricz, Generalized Bessel Functions of the First Kind, Lecture Notes in Mathematics 1994, Springer-Verlag, Berlin-Heidelberg, 2010.

5.
P. Cerone and S. S. Dragomir, Lobatto type quadrature rules for functions with bounded derivative, Math. Inequal. Appl. 3 (2000), no. 2, 197-209.

6.
B.-N. Guo and F. Qi, A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 72 (2010), no. 2, 21-30.

7.
B.-N. Guo and F. Qi, Some bounds for the complete elliptic integrals of the first and second kinds, Math. Inequal. Appl. 14 (2011), no. 2, 323-334.

8.
B.-N. Guo and F. Qi, Some inequalities and absolute monotonicity for modified Bessel functions of the first kind, ResearchGate Research, available online at http://dx.doi.org/10.13140/RG.2.1.3740.1129.

9.
E. K. Ifantis and P. D. Siafarikas, Inequalities involving Bessel and modified Bessel functions, J. Math. Anal. Appl. 147 (1990), no. 1, 214-227.

10.
Z. Liu, Note on a theorem of P. Cerone, Soochow J. Math. 32 (2006), no. 3, 323-326.

11.
Z. Liu and Y.-X. Shi, Note on Iyengar type integral inequalities, J. Anshan Univ. Sci. Tech. 26 (2003), no. 4, 318-320. (Chinese)

12.
Y. L. Luke, Inequalities for generalized hypergeometric functions, J. Approx. Theory 5 (1972), no. 1, 41-65.

13.
D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht-Boston-London, 1993.

14.
F. Qi, Inequalities for an integral, Math. Gaz. 80 (1996), no. 488, 376-377.

15.
F. Qi, Further generalizations of inequalities for an integral, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 8 (1997), 79-83.

16.
F. Qi, Polya type integral inequalities: origin, variants, proofs, refinements, generalizations, equivalences, and applications, Math. Inequal. Appl. 18 (2015), no. 1, 1-38.

17.
F. Qi, Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions, Math. Inequal. Appl. 18 (2015), no. 2, 493-518.

18.
F. Qi and C. Berg, Complete monotonicity of a difference between the exponential and trigamma functions and properties related to a modified Bessel function, Mediterr. J. Math. 10 (2013), no. 4, 1685-1696.

19.
F. Qi and W.-H. Li, A logarithmically completely monotonic function involving the ratio of gamma functions, J. Appl. Anal. Comput. 5 (2015), no. 4, 626-634.

20.
F. Qi, X.-T. Shi, F.-F. Liu, and Z.-H. Yang, A double inequality for an integral mean in terms of the exponential and logarithmic means, ResearchGate Research, available online at http://dx.doi.org/10.13140/RG.2.1.2353.6800.

21.
F. Qi and S.-H. Wang, Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions, Glob. J. Math. Anal. 2 (2014), no. 3, 91-97.

22.
R. L. Schilling, R. Song, and Z. Vondracek, Bernstein Functions-Theory and Applications, 2nd ed., de Gruyter Studies in Mathematics 37, Walter de Gruyter, Berlin, Germany, 2012.

23.
D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1946.