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Some conditions for a class of functions to be completely monotonic
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  • 作者:Senlin Guo (1)

    1. Department of Mathematics
    ; Zhongyuan University of Technology ; Zhengzhou ; Henan ; 450007 ; China
  • 关键词:34A40 ; 26D10 ; 26A48 ; necessary condition ; necessary and sufficient condition ; completely monotonic function ; gamma function
  • 刊名:Journal of Inequalities and Applications
  • 出版年:2015
  • 出版时间:December 2015
  • 年:2015
  • 卷:2015
  • 期:1
  • 全文大小:899 KB
  • 参考文献:1. Bernstein, S: Sur la d茅finition et les propri茅t茅s des fonctions analytiques d鈥檜ne variable r茅elle. Math. Ann. 75, 449-468 (1914) CrossRef
    2. Bernstein, S: Sur les fonctions absolument monotones. Acta Math. 51, 1-66 (1928) CrossRef
    3. Atanassov, RD, Tsoukrovski, UV: Some properties of a class of logarithmically completely monotonic functions. C. R. Acad. Bulgare Sci. 41, 21-23 (1988)
    4. Horn, RA: On infinitely divisible matrices, kernels, and functions. Z. Wahrscheinlichkeitstheor. Verw. Geb. 8, 219-230 (1967) CrossRef
    5. Guo, B-N, Qi, F: A class of completely monotonic functions involving divided differences of the psi and tri-gamma functions and some applications. J. Korean Math. Soc. 48, 655-667 (2011) CrossRef
    6. Guo, S: A class of logarithmically completely monotonic functions and their applications. J. Appl. Math. 2014, 757462 (2014)
    7. Guo, S: Logarithmically completely monotonic functions and applications. Appl. Math. Comput. 221, 169-176 (2013) CrossRef
    8. Guo, S: Some properties of completely monotonic sequences and related interpolation. Appl. Math. Comput. 219, 4958-4962 (2013) CrossRef
    9. Guo, S, Laforgia, A, Batir, N, Luo, Q-M: Completely monotonic and related functions: their applications. J. Appl. Math. 2014, 768516 (2014)
    10. Guo, S, Qi, F: A class of logarithmically completely monotonic functions associated with the gamma function. J.聽Comput. Appl. Math. 224, 127-132 (2009) CrossRef
    11. Guo, S, Qi, F, Srivastava, HM: A class of logarithmically completely monotonic functions related to the gamma function with applications. Integral Transforms Spec. Funct. 23, 557-566 (2012) CrossRef
    12. Guo, S, Qi, F, Srivastava, HM: Supplements to a class of logarithmically completely monotonic functions associated with the gamma function. Appl. Math. Comput. 197, 768-774 (2008) CrossRef
    13. Guo, S, Qi, F, Srivastava, HM: Necessary and sufficient conditions for two classes of functions to be logarithmically completely monotonic. Integral Transforms Spec. Funct. 18, 819-826 (2007) CrossRef
    14. Guo, S, Srivastava, HM: A certain function class related to the class of logarithmically completely monotonic functions. Math. Comput. Model. 49, 2073-2079 (2009) CrossRef
    15. Guo, S, Srivastava, HM: A class of logarithmically completely monotonic functions. Appl. Math. Lett. 21, 1134-1141 (2008) CrossRef
    16. Guo, S, Srivastava, HM, Batir, N: A certain class of completely monotonic sequences. Adv. Differ. Equ. 2013, 294 (2013) CrossRef
    17. Guo, S, Srivastava, HM, Cheung, WS: Some properties of functions related to certain classes of completely monotonic functions and logarithmically completely monotonic functions. Filomat 28, 821-828 (2014) CrossRef
    18. Krasniqi, VB, Srivastava, HM, Dragomir, SS: Some complete monotonicity properties for the \((p,q)\) -gamma function. Appl. Math. Comput. 219, 10538-10547 (2013) CrossRef
    19. Mortici, C: Completely monotone functions and the Wallis ratio. Appl. Math. Lett. 25, 717-722 (2012) CrossRef
    20. Qi, F, Luo, Q-M: Bounds for the ratio of two gamma functions - from Wendel鈥檚 and related inequalities to logarithmically completely monotonic functions. Banach J. Math. Anal. 6, 132-158 (2012) CrossRef
    21. Qi, F, Luo, Q-M, Guo, B-N: Complete monotonicity of a function involving the divided difference of digamma functions. Sci. China Math. 56, 2315-2325 (2013) CrossRef
    22. Salem, A: An infinite class of completely monotonic functions involving the / q-gamma function. J. Math. Anal. Appl. 406, 392-399 (2013) CrossRef
    23. Salem, A: A completely monotonic function involving / q-gamma and / q-digamma functions. J. Approx. Theory 164, 971-980 (2012) CrossRef
    24. Sevli, H, Batir, N: Complete monotonicity results for some functions involving the gamma and polygamma functions. Math. Comput. Model. 53, 1771-1775 (2011) CrossRef
    25. Shemyakova, E, Khashin, SI, Jeffrey, DJ: A conjecture concerning a completely monotonic function. Comput. Math. Appl. 60, 1360-1363 (2010) CrossRef
    26. Wei, C-F, Guo, B-N: Complete monotonicity of functions connected with the exponential function and derivatives. Abstr. Appl. Anal. 2014, 851213 (2014)
    27. Yang, S: Absolutely (completely) monotonic functions and Jordan-type inequalities. Appl. Math. Lett. 25, 571-574 (2012) CrossRef
    28. Srivastava, HM, Guo, S, Qi, F: Some properties of a class of functions related to completely monotonic functions. Comput. Math. Appl. 64, 1649-1654 (2012) CrossRef
    29. Erd茅lyi, A (ed.): Higher Transcendental Functions, vol.聽1. McGraw-Hill, New York (1953)
  • 刊物主题:Analysis; Applications of Mathematics; Mathematics, general;
  • 出版者:Springer International Publishing
  • ISSN:1029-242X
文摘
In this article, we present a necessary condition and a necessary and sufficient condition for a class of functions to be completely monotonic.

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