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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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 46; no. 4
Main Authors Mao, Zhong-Xuan, Tian, Jing-Feng
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.07.2023
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Multivariate analysis
Time
33B15
Completely monotonic degree
Time scales
Absolute monotonicity
Primary 26A48
Secondary 26E70
Logarithmic complete monotonicity
26B25
Complete monotonicity
Psi function
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Summary: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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ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01533-y