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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2025 / Volume: 54 Issue: 6

Strongly completely monotonic functions on time scales

Jing-feng Tian(North China Electric Power University)0000-0002-0631-038X
Xiao-yue Du(North China Electric Power University)0009-0003-7792-6231
Zhong-xuan Mao(North China Electric Power University)0000-0001-5089-301X
Jun-yi Li(Northwestern Polytechnical University)0009-0006-6010-2174
Sayfa
—
Yayın Tarihi
2025-12-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

As applications, we prove that certain functions involving the confluent and Gaussian hypergeometric functions are strongly completely monotonic.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we introduce the concept of strongly completely monotonic functions on time scales and investigate several properties of such functions.
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Temel Bulgular & Veri:Meanwhile, we present some key results considering three special cases including continuous, discrete, and quantum.
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Sonuç & Katkı:As applications, we prove that certain functions involving the confluent and Gaussian hypergeometric functions are strongly completely monotonic.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:time scales · strongly completely monotonic function · completely monotonic function

Abstract

In this paper, we introduce the concept of strongly completely monotonic functions on time scales and investigate several properties of such functions. Meanwhile, we present some key results considering three special cases including continuous, discrete, and quantum. As applications, we prove that certain functions involving the confluent and Gaussian hypergeometric functions are strongly completely monotonic.

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Bu Makaleye Atıf Yap

Tian, J., Du, X., Mao, Z., Li, J. (2025). Strongly completely monotonic functions on time scales. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 6. https://doi.org/10.15672/hujms.1597774

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Kaynakça (26)

  1. K. Aomoto and M. Kita, Theory of hypergeometric functions, Springer Monographs Math, Tokyo, 2011.
  2. F.M. Atici, D.C. Biles and A. Lebedinsky, An application of time scales to economics, Math. Comput. Model. 43, 718–726, 2006.
  3. F.M. Atici and F. Uysal, A production-inventory model of HMMS on time scales, Appl. Math. Lett. 21, 236–243, 2008.
  4. S. Bernstein, Sur les fonctions absolument monotones(French), Acta Math. 52, 1–66, 1929.
  5. M. Bohner, Dynamic equations on time scales: An Introduction with Applications, Birkhauser, 2001.
  6. M. Bohner and B. Karpuz, The gamma function on time scales, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20(4), 507–522, 2013.
  7. M. Bohner and A. Peterson, Laplace transform and Z-transform: unification and extension, Meth. Appl. Anal. 9(1), 151–158, 2002.
  8. R. Boucekkine and J. R. Ruiz-Tamarit, Special functions for the study of economic dynamics: the case of the Lucas-Uzawa model, J. Math. Econom. 44(1), 33–54, 2008.
  9. Y.A. Brychkov and N.V. Savischenko, Application of hypergeometric functions of two variables in wireless communication theory, Lobachevskii. J. Math. 40, 938–953, 2019.
  10. R. Chandramouli and N. Ranganathan, Computing the bivariate gaussian probability integral, IEEE Signal Proc. 6(6), 129–131, 1999.
  11. B.-N. Guo and F. Qi, A completely monotonic function involving the tri-gamma function and with degree one, Appl. Math. Comput. 218(19), 9890–9897, 2012.
  12. S. Hilger, Ein maßkettenkalkül mit anwendung auf zentrumsmannigfaltigkeiten, PhD thesis, 1988.
  13. S. Hilger, Analysis on measure chains-A unified approach to continuous and discrete calculus, Results. Math. 18, 18–56, 1990.
  14. S. Koumandos and H.L. Pedersen, Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma function, J. Math. Anal. Appl. 355(1), 33–40, 2009.
  15. V. Lakshmilkantham and S. Sivasundaramn, Stability of moving invariant sets and uncertain dynamic systems on time scales, Comput. Math. Appl. 36(10-12), 339–346, 1998.
  16. Z.-X. Mao and J.-F. Tian, Delta complete monotonicity and completely monotonic degree on time scales, Bull. Malays. Math. Sci. Soc. 46(4), 142, 2023.
  17. Z.-X. Mao and J.-F. Tian, Delta L’Hospital-, Laplace- and variable limit-type monotonicity rules on time scales, Bull. Malays. Math. Sci. Soc. 47(1), 1, 2024.
  18. Z.-X. Mao, J.-F. Tian and Y.-R. Zhu, Psi, polygamma functions and Q-complete monotonicity on time scales, J. Appl. Anal. Comput. 13(3), 1137–1154, 2023.
  19. B. Martin and G.S. Guseinov, The convolution on time scales, Abstr. Appl. Anal. 2007(3–4), 2007.
  20. N. Michel and M.V. Stoitsov, Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Poschl-Teller-Ginocchio potential wave functions, Comput. Physics. Commun. 178(7), 535–551, 2008.
  21. Q. Sheng, M. Fadag, J. Henderson and J.M. Davis, An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Anal. Real World Appl. 7(3), 395–413, 2006.
  22. X. Tian and Y. Zhang, Fractional time-scales Noether theorem with Caputo $\Delta$- derivatives for Hamiltonian systems, Appl. Math. Comput. 393, 125753, 2021.
  23. S.Y. Trimble, J. Wells and F.T. Wright, Superadditive functions and a statistical application, SIAM J. Math. Anal. 20(5), 1255–1259, 1989.
  24. D.V. Widder, The Laplace transform, Princeton Mathematical Series, vol. 6. Princeton University Press, Princeton, 1941.
  25. J.-F. Xu, B. Pervaiz, A. Zada, et al., Stability analysis of causal integral evolution impulsive systems on time scales, Acta. Math. Sci. 41, 781–800, 2021.
  26. L. Zhu, A class of strongly completely monotonic functions related to gamma function, J. Comput. Appl. Math. 367, 112–469, 2020.