Some conditions for sequences to be minimal completely monotonic

Xifeng Wang; Senlin Guo; Xifeng Wang; Senlin Guo

doi:10.3934/math.2023496

AIMS Mathematics

2023, Volume 8, Issue 4: 9832-9839. doi: 10.3934/math.2023496

Previous Article Next Article

Research article

Some conditions for sequences to be minimal completely monotonic

Xifeng Wang ^,,
Senlin Guo

College of Science, Zhongyuan University of Technology, Zhengzhou, Henan 450007, China

Received: 07 November 2022 Revised: 30 January 2023 Accepted: 06 February 2023 Published: 22 February 2023
MSC : 44A60, 44A10

In this article, we establish some necessary conditions for sequences to be minimal completely monotonic. We also present some properties for completely monotonic sequences.
- completely monotonic sequence,
- completely monotonic function,
- Hausdorff Theorem,
- minimal completely monotonic sequence
Citation: Xifeng Wang, Senlin Guo. Some conditions for sequences to be minimal completely monotonic[J]. AIMS Mathematics, 2023, 8(4): 9832-9839. doi: 10.3934/math.2023496

Related Papers:

Abstract

In this article, we establish some necessary conditions for sequences to be minimal completely monotonic. We also present some properties for completely monotonic sequences.

References

[1]	S. Bernstein, Sur la d'efinition et les propri'et'es des fonctions analytiques d'une variable r'eelle, Math. Ann., 75 (1914), 449–468.
[2]	S. Guo, Some properties of functions related to completely monotonic functions, Filomat, 31 (2017), 247–254. https://doi.org/10.2298/FIL1702247G doi: 10.2298/FIL1702247G
[3]	S. Guo, On completely monotonic and related functions, Filomat, 30 (2016), 2083–2090. https://doi.org/10.2298/FIL1607083G doi: 10.2298/FIL1607083G
[4]	S. Guo, Some conditions for a class of functions to be completely monotonic, J. Inequal. Appl., 2015 (2015), 11. https://doi.org/10.1186/s13660-014-0534-y doi: 10.1186/s13660-014-0534-y
[5]	S. Guo, Some properties of completely monotonic sequences and related interpolation, Appl. Math. Comput., 219 (2013), 4958–4962. https://dx.doi.org/10.1016/j.amc.2012.11.073
[6]	S. Guo, H. M. Srivastava, N. Batir, A certain class of completely monotonic sequences, Adv. Differ. Equ., 2013 (2013), 294. https://doi.org/10.1186/1687-1847-2013-294 doi: 10.1186/1687-1847-2013-294
[7]	S. Guo, H. M. Srivastava, W. S. Cheung, Some properties of functions related to certain classes of completely monotonic functions and logarithmically completely monotonic functions, Filomat, 28 (2014), 821–828. https://doi.org/10.2298/FIL1404821G doi: 10.2298/FIL1404821G
[8]	F. Hausdorff, Summationsmethoden und momentfolgen I, Math. Z., 9 (1921), 74–109.
[9]	L. Lorch, L. Moser, A remark on completely monotonic sequences, with an application to summability, Canad. Math. Bull., 6 (1963), 171–173.
[10]	L. Lorch, D. J. Newman, On the composition of completely monotonic functions, completely monotonic sequences and related questions, J. London Math. Soc., 28 (1983), 31–45.
[11]	F. Qi, Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic, Math. Inequal. Appl., 24 (2021), 845–855. https://doi.org/10.7153/mia-2021-24-58 doi: 10.7153/mia-2021-24-58
[12]	F. Qi, Completely monotonic degree of a function involving trigamma and tetragamma functions, AIMS Math., 5 (2020), 3391–3407. https://doi.org/10.3934/math.2020219 doi: 10.3934/math.2020219
[13]	F. Qi, R. P. Agarwal, On complete monotonicity for several classes of functions related to ratios of gamma functions, J. Inequal. Appl., 2019 (2019), 36. https://doi.org/10.1186/s13660-019-1976-z doi: 10.1186/s13660-019-1976-z
[14]	F. Qi, D. W. Niu, Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions, Appl. Anal. Discrete Math., 14 (2020), 512–527. https://doi.org/10.2298/AADM191111033Q doi: 10.2298/AADM191111033Q
[15]	X. F.Wang, M. Ismail, N. Batir, S. Guo, A necessary and sufficient condition for sequences to be minimal completely monotonic, Adv. Difference Equ., 2020 (2020), 665. https://doi.org/10.1186/s13662-020-03051-8 doi: 10.1186/s13662-020-03051-8
[16]	A. M. Xu, Z. D.Cen, Qi's conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and tri-gamma functions, J. Inequal. Appl., 2020 (2020), 83. https://doi.org/10.1186/s13660-020-02345-5 doi: 10.1186/s13660-020-02345-5
[17]	Z. H. Yang, J. F. Tian, Monotonicity rules for the ratio of two Laplace transforms with applications, J. Math. Anal. Appl., 470 (2019), 821–845. https://doi.org/10.1016/j.jmaa.2018.10.034 doi: 10.1016/j.jmaa.2018.10.034
[18]	Z. H. Yang, Y. M. Chu, Monotonicity and inequalities involving the modified Bessel functions of the second kind, J. Math. Anal. Appl., 508 (2022), 125889. https://doi.org/10.1016/j.jmaa.2021.125889 doi: 10.1016/j.jmaa.2021.125889
[19]	D. V. Widder, Necessary and sufficient conditions for the representation of a function as a Laplace integral, Trans. Amer. Math. Soc., 33 (1931), 851–892.
[20]	D. V. Widder, The Laplace transform, Princeton: Princeton University Press, 1941.
[21]	J. Wimp, Sequence transformations and their applications, New York: Academic Press, 1981.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)