Delta Complete Monotonicity and Completely Monotonic Degree on Time Scales
The theory of time scale was proposed to unite continuous and discrete statements. In this paper, we introduce the concepts of complete monotonicity, logarithmic complete monotonicity, and absolute monotonicity of multivariate functions on time scales utilizing the delta derivative. Following that,...
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| Published in | Bulletin of the Malaysian Mathematical Sciences Society Vol. 46; no. 4 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.07.2023
Springer Nature B.V |
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| Abstract | The theory of time scale was proposed to unite continuous and discrete statements. In this paper, we introduce the concepts of complete monotonicity, logarithmic complete monotonicity, and absolute monotonicity of multivariate functions on time scales utilizing the delta derivative. Following that, we investigate the properties of delta complete monotonicity on time scales and present some judgment rules. Using judgment rules, three functions are shown to be delta complete monotonicity on time scales. And then, in order to quantitatively measure two delta completely monotonic functions on time scales, we present the concept of completely monotonic degree of univariate and multivariate functions on time scales and explore some properties of them. |
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| AbstractList | The theory of time scale was proposed to unite continuous and discrete statements. In this paper, we introduce the concepts of complete monotonicity, logarithmic complete monotonicity, and absolute monotonicity of multivariate functions on time scales utilizing the delta derivative. Following that, we investigate the properties of delta complete monotonicity on time scales and present some judgment rules. Using judgment rules, three functions are shown to be delta complete monotonicity on time scales. And then, in order to quantitatively measure two delta completely monotonic functions on time scales, we present the concept of completely monotonic degree of univariate and multivariate functions on time scales and explore some properties of them. |
| ArticleNumber | 142 |
| Author | Mao, Zhong-Xuan Tian, Jing-Feng |
| Author_xml | – sequence: 1 givenname: Zhong-Xuan surname: Mao fullname: Mao, Zhong-Xuan organization: Hebei Key Laboratory of Physics and Energy Technology, Department of Mathematics and Physics, North China Electric Power University – sequence: 2 givenname: Jing-Feng orcidid: 0000-0002-0631-038X surname: Tian fullname: Tian, Jing-Feng email: tianjf@ncepu.edu.cn organization: Hebei Key Laboratory of Physics and Energy Technology, Department of Mathematics and Physics, North China Electric Power University |
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| Cites_doi | 10.1007/s11425-016-0070-y 10.1016/j.mcm.2005.08.014 10.1186/s13660-017-1527-4 10.5802/crmath.399 10.1007/s40840-021-01224-6 10.1007/978-1-4612-0201-1 10.1090/S0025-5718-1986-0856710-6 10.4134/BKMS.2010.47.1.103 10.1016/j.aml.2007.03.013 10.1007/978-3-319-47620-9 10.1016/j.jmaa.2017.05.081 10.1007/s40840-016-0435-y 10.1007/s40840-015-0300-4 10.1007/s13398-020-00992-3 10.1007/s40840-014-0096-7 10.1007/s40840-017-0595-4 10.4310/CMS.2003.v1.n1.a8 10.1007/BF02592679 10.1016/0022-247X(86)90042-9 10.1016/j.jmaa.2016.04.029 10.1007/s11425-014-4917-9 10.1007/s40840-019-00871-0 10.1007/s10473-021-0310-2 10.1007/s13398-018-0609-6 10.1525/9780520345294 10.1007/978-0-8176-8230-9 10.3934/math.2020224 10.1016/j.nahs.2018.12.005 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | 33B15 Completely monotonic degree Time scales Absolute monotonicity Primary 26A48 Secondary 26E70 Logarithmic complete monotonicity 26B25 Complete monotonicity Psi function |
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| References | TianXZhangYFractional time-scales Noether theorem with Caputo Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}-derivatives for Hamiltonian systemsAppl. Math. Comput.202139312575341769551508.70025 KayarZKaymakçalanBNovel diamond alpha Bennett–Leindler type dynamic inequalities and their applicationsBull. Malays. Math. Sci. Soc.20224510271054441230810.1007/s40840-021-01224-61497.26022 YangZ-HZhengS-ZComplete monotonicity and inequalites involving Gurland’s ratios of gamma functionsMath. Inequal. Appl.2019229710939059731416.33005 Brito da CruzAMCMartinsNTorresDFMThe diamond integral on time scalesBull. Malays. Math. Sci. Soc.20153814531462339383110.1007/s40840-014-0096-71326.26039 BohnerMPetersonADynamic equations on time scales2001BostonSpringer10.1007/978-1-4612-0201-10978.39001 AticiFMBilesDCLebedinskyAAn application of time scales to economicsMath. Comput. Model.200643718726221831510.1016/j.mcm.2005.08.0141187.91125 BohnerMStreipertSTorresDFMExact solution to a dynamic SIR modelNonlear Anal. Hybri.201932228238389510510.1016/j.nahs.2018.12.0051425.92177 DengXWangQZhouZOscillation criteria for second order neutral dynamic equations of Emden–Fowler type with positive and negative coefficients on time scalesSci. China Math.201760113132358505310.1007/s11425-016-0070-y1370.34146 AbramowitzMStegunIAHandbook of mathematical functions with formulas, graphs, and mathematical tables1992New YorkDover Publications0171.38503 ZhangCAgarwalRPBohnerMOscillation of fourth-order delay dynamic equationsSci. China Math.201558143160329633610.1007/s11425-014-4917-91321.34121 YangZ-HZhengS-ZComplete monotonicity involving some ratios of gamma functionsJ. Inequal. Appl.20172017255371162910.1186/s13660-017-1527-41372.33002 TianJ-FZhuY-RCheungW-SN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}-tuple Diamond-Alpha integral and inequalities on time scalesRev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM201911321892200395624310.1007/s13398-018-0609-61429.26048 MaoZ-XTianJ-FMonotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kindC. R. Math. Acad. Sci. Paris2023361217235453854707652644 IsmailMEHCompletely monotonic functions associated with the gamma function and its q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analoguesJ. Math. Anal. Appl.19881161983733710.1016/0022-247X(86)90042-9 QiuY-CWangQ-RExistence of nonoscillatory solutions to higher-order nonlinear neutral dynamic equations on time scalesBull. Malays. Math. Sci. Soc.20184119351952385450010.1007/s40840-016-0435-y1406.34110 YuXWangQWeighted Pseudo-Almost periodic solutions for shunting inhibitory cellular neural networks on time scalesBull. Malays. Math. Sci. Soc.20194220552074398440910.1007/s40840-017-0595-41450.34072 BustozJIsmailMEHOn gamma function inequalitiesMath. Comp.19864765966785671010.1090/S0025-5718-1986-0856710-60607.33002 Hilger, S.: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. PhD thesis, Universität Würzburg, Würzburg, Germany (1988) BochnerSHarmonic analysis and the theory of probability1955Berkeley and Los AngelesUniversity of California Press10.1525/97805203452940068.11702 ZhaoT-HWangM-KChuY-MMonotonicity and convexity involving generalized elliptic integral of the first kindRev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM202111546419743710.1007/s13398-020-00992-31456.33016 BernsteinSSur les fonctions absolument monotones(French)Acta Math.192952166155526910.1007/BF0259267955.0142.07 ZhuLCompletely monotonic integer degrees for a class of special functionsAIMS Math.2020534563471414610710.3934/math.20202241484.33007 WeinanEEngquistBThe heterognous multiscale methodsCommun. Math. Sci.2003187132197984610.4310/CMS.2003.v1.n1.a81093.35012 YangZ-HApproximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma functionJ. Math. Anal. Appl.2016441549564349154210.1016/j.jmaa.2016.04.0291336.33005 BohnerMPetersonAAdvances in dynamic equations on time scales2003BostonSpringer10.1007/978-0-8176-8230-91025.34001 BohnerMGeorgievSGMultivariable dynamic calculus on time scales2016ChamSpriner10.1007/978-3-319-47620-91475.26001 GuoB-NQiFTwo new proofs of the complete monotonicity of a function involving the psi functionBull. Korean Math. Soc.201047103111260423610.4134/BKMS.2010.47.1.1031183.33002 WeinanEPrinciples of multiscale modeling2011CambridgeCambridge University Press1238.00010 XuJ-FPervaizBZadaAStability analysis of causal integral evolution impulsive systems on time scalesActa. Math. Sci.202141781800424543310.1007/s10473-021-0310-207557576 AticiFMUysalFA production-inventory model of HMMS on time scalesAppl. Math. Lett.200821236243243373410.1016/j.aml.2007.03.0131153.90001 MalikMKumarVExistence, stability and controllability results of coupled fractional dynamical system on time scalesBull. Malays. Math. Sci. Soc.20204333693394415283610.1007/s40840-019-00871-01478.34098 SakerSHO’ReganDHardy and Littlewood inequalities on time scalesBull. Malays. Math. Sci. Soc.201639527543347132910.1007/s40840-015-0300-41342.26065 WidderDVThe Laplace Transform, Princeton Mathematical Series1941PrincetonPrinceton University Press YangZ-HSome properties of the divided difference of psi and polygamma functionsJ. Math. Anal. Appl.2017455761777366513110.1016/j.jmaa.2017.05.0811369.33007 X Deng (1533_CR9) 2017; 60 Z-X Mao (1533_CR30) 2023; 361 M Bohner (1533_CR20) 2016 DV Widder (1533_CR22) 1941 Z-H Yang (1533_CR27) 2017; 2017 M Malik (1533_CR12) 2020; 43 E Weinan (1533_CR14) 2011 M Bohner (1533_CR6) 2001 L Zhu (1533_CR32) 2020; 5 Y-C Qiu (1533_CR11) 2018; 41 FM Atici (1533_CR17) 2006; 43 Z-H Yang (1533_CR28) 2019; 22 E Weinan (1533_CR13) 2003; 1 FM Atici (1533_CR18) 2008; 21 M Bohner (1533_CR19) 2019; 32 M Bohner (1533_CR7) 2003 AMC Brito da Cruz (1533_CR2) 2015; 38 1533_CR1 J-F Tian (1533_CR8) 2019; 113 S Bochner (1533_CR31) 1955 X Yu (1533_CR4) 2019; 42 M Abramowitz (1533_CR33) 1992 Z Kayar (1533_CR5) 2022; 45 S Bernstein (1533_CR21) 1929; 52 T-H Zhao (1533_CR29) 2021; 115 J Bustoz (1533_CR23) 1986; 47 C Zhang (1533_CR10) 2015; 58 B-N Guo (1533_CR34) 2010; 47 Z-H Yang (1533_CR26) 2017; 455 SH Saker (1533_CR3) 2016; 39 Z-H Yang (1533_CR25) 2016; 441 MEH Ismail (1533_CR24) 1988; 116 J-F Xu (1533_CR16) 2021; 41 X Tian (1533_CR15) 2021; 393 |
| References_xml | – reference: Brito da CruzAMCMartinsNTorresDFMThe diamond integral on time scalesBull. Malays. Math. Sci. Soc.20153814531462339383110.1007/s40840-014-0096-71326.26039 – reference: WeinanEEngquistBThe heterognous multiscale methodsCommun. Math. Sci.2003187132197984610.4310/CMS.2003.v1.n1.a81093.35012 – reference: KayarZKaymakçalanBNovel diamond alpha Bennett–Leindler type dynamic inequalities and their applicationsBull. Malays. Math. Sci. Soc.20224510271054441230810.1007/s40840-021-01224-61497.26022 – reference: AticiFMBilesDCLebedinskyAAn application of time scales to economicsMath. Comput. Model.200643718726221831510.1016/j.mcm.2005.08.0141187.91125 – reference: YangZ-HZhengS-ZComplete monotonicity involving some ratios of gamma functionsJ. Inequal. Appl.20172017255371162910.1186/s13660-017-1527-41372.33002 – reference: BernsteinSSur les fonctions absolument monotones(French)Acta Math.192952166155526910.1007/BF0259267955.0142.07 – reference: BohnerMPetersonAAdvances in dynamic equations on time scales2003BostonSpringer10.1007/978-0-8176-8230-91025.34001 – reference: QiuY-CWangQ-RExistence of nonoscillatory solutions to higher-order nonlinear neutral dynamic equations on time scalesBull. Malays. Math. Sci. Soc.20184119351952385450010.1007/s40840-016-0435-y1406.34110 – reference: MalikMKumarVExistence, stability and controllability results of coupled fractional dynamical system on time scalesBull. Malays. Math. Sci. Soc.20204333693394415283610.1007/s40840-019-00871-01478.34098 – reference: MaoZ-XTianJ-FMonotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kindC. R. Math. Acad. Sci. Paris2023361217235453854707652644 – reference: BohnerMGeorgievSGMultivariable dynamic calculus on time scales2016ChamSpriner10.1007/978-3-319-47620-91475.26001 – reference: ZhaoT-HWangM-KChuY-MMonotonicity and convexity involving generalized elliptic integral of the first kindRev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM202111546419743710.1007/s13398-020-00992-31456.33016 – reference: DengXWangQZhouZOscillation criteria for second order neutral dynamic equations of Emden–Fowler type with positive and negative coefficients on time scalesSci. China Math.201760113132358505310.1007/s11425-016-0070-y1370.34146 – reference: AticiFMUysalFA production-inventory model of HMMS on time scalesAppl. Math. Lett.200821236243243373410.1016/j.aml.2007.03.0131153.90001 – reference: YuXWangQWeighted Pseudo-Almost periodic solutions for shunting inhibitory cellular neural networks on time scalesBull. Malays. Math. Sci. Soc.20194220552074398440910.1007/s40840-017-0595-41450.34072 – reference: ZhangCAgarwalRPBohnerMOscillation of fourth-order delay dynamic equationsSci. China Math.201558143160329633610.1007/s11425-014-4917-91321.34121 – reference: BohnerMPetersonADynamic equations on time scales2001BostonSpringer10.1007/978-1-4612-0201-10978.39001 – reference: IsmailMEHCompletely monotonic functions associated with the gamma function and its q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analoguesJ. Math. Anal. Appl.19881161983733710.1016/0022-247X(86)90042-9 – reference: BochnerSHarmonic analysis and the theory of probability1955Berkeley and Los AngelesUniversity of California Press10.1525/97805203452940068.11702 – reference: WidderDVThe Laplace Transform, Princeton Mathematical Series1941PrincetonPrinceton University Press – reference: YangZ-HZhengS-ZComplete monotonicity and inequalites involving Gurland’s ratios of gamma functionsMath. Inequal. Appl.2019229710939059731416.33005 – reference: WeinanEPrinciples of multiscale modeling2011CambridgeCambridge University Press1238.00010 – reference: XuJ-FPervaizBZadaAStability analysis of causal integral evolution impulsive systems on time scalesActa. Math. Sci.202141781800424543310.1007/s10473-021-0310-207557576 – reference: ZhuLCompletely monotonic integer degrees for a class of special functionsAIMS Math.2020534563471414610710.3934/math.20202241484.33007 – reference: YangZ-HSome properties of the divided difference of psi and polygamma functionsJ. Math. Anal. Appl.2017455761777366513110.1016/j.jmaa.2017.05.0811369.33007 – reference: BohnerMStreipertSTorresDFMExact solution to a dynamic SIR modelNonlear Anal. Hybri.201932228238389510510.1016/j.nahs.2018.12.0051425.92177 – reference: SakerSHO’ReganDHardy and Littlewood inequalities on time scalesBull. Malays. Math. Sci. Soc.201639527543347132910.1007/s40840-015-0300-41342.26065 – reference: BustozJIsmailMEHOn gamma function inequalitiesMath. Comp.19864765966785671010.1090/S0025-5718-1986-0856710-60607.33002 – reference: Hilger, S.: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. PhD thesis, Universität Würzburg, Würzburg, Germany (1988) – reference: TianJ-FZhuY-RCheungW-SN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}-tuple Diamond-Alpha integral and inequalities on time scalesRev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM201911321892200395624310.1007/s13398-018-0609-61429.26048 – reference: YangZ-HApproximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma functionJ. Math. Anal. Appl.2016441549564349154210.1016/j.jmaa.2016.04.0291336.33005 – reference: GuoB-NQiFTwo new proofs of the complete monotonicity of a function involving the psi functionBull. Korean Math. Soc.201047103111260423610.4134/BKMS.2010.47.1.1031183.33002 – reference: TianXZhangYFractional time-scales Noether theorem with Caputo Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}-derivatives for Hamiltonian systemsAppl. Math. Comput.202139312575341769551508.70025 – reference: AbramowitzMStegunIAHandbook of mathematical functions with formulas, graphs, and mathematical tables1992New YorkDover Publications0171.38503 – volume: 60 start-page: 113 year: 2017 ident: 1533_CR9 publication-title: Sci. China Math. doi: 10.1007/s11425-016-0070-y – volume: 43 start-page: 718 year: 2006 ident: 1533_CR17 publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2005.08.014 – ident: 1533_CR1 – volume: 2017 start-page: 255 year: 2017 ident: 1533_CR27 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-017-1527-4 – volume: 393 start-page: 125753 year: 2021 ident: 1533_CR15 publication-title: Appl. Math. Comput. – volume: 361 start-page: 217 year: 2023 ident: 1533_CR30 publication-title: C. R. Math. Acad. Sci. Paris doi: 10.5802/crmath.399 – volume: 45 start-page: 1027 year: 2022 ident: 1533_CR5 publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-021-01224-6 – volume-title: Dynamic equations on time scales year: 2001 ident: 1533_CR6 doi: 10.1007/978-1-4612-0201-1 – volume: 47 start-page: 659 year: 1986 ident: 1533_CR23 publication-title: Math. Comp. doi: 10.1090/S0025-5718-1986-0856710-6 – volume: 47 start-page: 103 year: 2010 ident: 1533_CR34 publication-title: Bull. Korean Math. Soc. doi: 10.4134/BKMS.2010.47.1.103 – volume: 21 start-page: 236 year: 2008 ident: 1533_CR18 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2007.03.013 – volume-title: Multivariable dynamic calculus on time scales year: 2016 ident: 1533_CR20 doi: 10.1007/978-3-319-47620-9 – volume: 455 start-page: 761 year: 2017 ident: 1533_CR26 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.05.081 – volume-title: The Laplace Transform, Princeton Mathematical Series year: 1941 ident: 1533_CR22 – volume-title: Principles of multiscale modeling year: 2011 ident: 1533_CR14 – volume: 41 start-page: 1935 year: 2018 ident: 1533_CR11 publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-016-0435-y – volume-title: Handbook of mathematical functions with formulas, graphs, and mathematical tables year: 1992 ident: 1533_CR33 – volume: 39 start-page: 527 year: 2016 ident: 1533_CR3 publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-015-0300-4 – volume: 115 start-page: 46 year: 2021 ident: 1533_CR29 publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM doi: 10.1007/s13398-020-00992-3 – volume: 38 start-page: 1453 year: 2015 ident: 1533_CR2 publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-014-0096-7 – volume: 42 start-page: 2055 year: 2019 ident: 1533_CR4 publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-017-0595-4 – volume: 1 start-page: 87 year: 2003 ident: 1533_CR13 publication-title: Commun. Math. Sci. doi: 10.4310/CMS.2003.v1.n1.a8 – volume: 52 start-page: 1 year: 1929 ident: 1533_CR21 publication-title: Acta Math. doi: 10.1007/BF02592679 – volume: 116 start-page: 1 year: 1988 ident: 1533_CR24 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(86)90042-9 – volume: 441 start-page: 549 year: 2016 ident: 1533_CR25 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2016.04.029 – volume: 58 start-page: 143 year: 2015 ident: 1533_CR10 publication-title: Sci. China Math. doi: 10.1007/s11425-014-4917-9 – volume: 43 start-page: 3369 year: 2020 ident: 1533_CR12 publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-019-00871-0 – volume: 41 start-page: 781 year: 2021 ident: 1533_CR16 publication-title: Acta. Math. Sci. doi: 10.1007/s10473-021-0310-2 – volume: 113 start-page: 2189 year: 2019 ident: 1533_CR8 publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM doi: 10.1007/s13398-018-0609-6 – volume-title: Harmonic analysis and the theory of probability year: 1955 ident: 1533_CR31 doi: 10.1525/9780520345294 – volume-title: Advances in dynamic equations on time scales year: 2003 ident: 1533_CR7 doi: 10.1007/978-0-8176-8230-9 – volume: 22 start-page: 97 year: 2019 ident: 1533_CR28 publication-title: Math. Inequal. Appl. – volume: 5 start-page: 3456 year: 2020 ident: 1533_CR32 publication-title: AIMS Math. doi: 10.3934/math.2020224 – volume: 32 start-page: 228 year: 2019 ident: 1533_CR19 publication-title: Nonlear Anal. Hybri. doi: 10.1016/j.nahs.2018.12.005 |
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| Snippet | The theory of time scale was proposed to unite continuous and discrete statements. In this paper, we introduce the concepts of complete monotonicity,... |
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| SubjectTerms | Applications of Mathematics Mathematics Mathematics and Statistics Multivariate analysis Time |
| Title | Delta Complete Monotonicity and Completely Monotonic Degree on Time Scales |
| URI | https://link.springer.com/article/10.1007/s40840-023-01533-y https://www.proquest.com/docview/2825839952 |
| Volume | 46 |
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