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 in:Bulletin of the Malaysian Mathematical Sciences Society 2023-07, Vol.46 (4), Article 142
Main Authors: Mao, Zhong-Xuan, Tian, Jing-Feng
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Multivariate analysis
Time
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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.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01533-y