Absolute monotonicity of a function involving the exponential function

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In the paper, the author verifies the absolute monotonicity of a function involving the exponential function.

    Keywords: absolute monotonicity; absolutely monotonic function; completely monotonic function; completely monotonic degree; exponential function

    MSC: Primary 26A48; Secondary 33B10, 44A10


  • References


    1. B.-N. Guo and F. Qi, A completely monotonic function involving the tri-gamma function and with degree one, Appl. Math. Comput. 218 (2012), no. 19, 9890--9897; Available online at http://dx.doi.org/10.1016/j.amc.2012.03.075.
    2. 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.
    3. B.-N. Guo and F. Qi, On the degree of the weighted geometric mean as a complete Bernstein function, Afr. Mat. 26 (2015), in press; Available online at http://dx.doi.org/10.1007/s13370-014-0279-2.
    4. B.-N. Guo, J.-L. Zhao, and F. Qi, A completely monotonic function involving the tri- and tetra-gamma functions, Math. Slovaca 63 (2013), no. 3, 469--478; Available online at http://dx.doi.org/10.2478/s12175-013-0109-2.
    5. D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht-Boston-London, 1993.
    6. F. Qi, A completely monotonic function related to the -trigamma function, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 76 (2014), no. 1, 107--114.
    7. F. Qi, A method of constructing inequalities about , Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 8 (1997), 16--23.
    8. F. Qi, Completely monotonic degree of a function involving the tri- and tetra-gamma functions, available online at http://arxiv.org/abs/1301.0154v3.
    9. F. Qi, Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function, J. Comput. Appl. Math. 268 (2014), 155--167; Available online at http://dx.doi.org/10.1016/j.cam.2014.03.004.
    10. F. Qi, Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions, Math. Inequal. Appl. 18 (2015), in press; Available online at http://arxiv.org/abs/1302.6731.
    11. F. Qi, P. Cerone, and S. S. Dragomir, Complete monotonicity of a function involving the divided difference of psi functions, Bull. Aust. Math. Soc. 88 (2013), no. 2, 309--319; Available online at http://dx.doi.org/10.1017/S0004972712001025.
    12. F. Qi and W.-H. Li, A logarithmically completely monotonic function involving the ratio of two gamma functions and originating from the coding gain, available online at http://arxiv.org/abs/1303.1877.
    13. F. Qi, Q.-M. Luo, and B.-N. Guo, Complete monotonicity of a function involving the divided difference of digamma functions, Sci. China Math. 56 (2013), no. 11, 2315--2325; Available online at http://dx.doi.org/10.1007/s11425-012-4562-0.
    14. 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; Available online at http://dx.doi.org/10.14419/gjma.v2i3.2919.
    15. R. L. Schilling, R. Song, and Z. Vondra?ek, Bernstein Functions---Theory and Applications, 2nd ed., de Gruyter Studies in Mathematics 37, Walter de Gruyter, Berlin, Germany, 2012; Available online at http://dx.doi.org/10.1515/9783110269338.
    16. D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1946.

 

View

Download

Article ID: 3062
 
DOI: 10.14419/gjma.v2i3.3062




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.