Delta L’Hospital-, Laplace- and Variable Limit-Type Monotonicity Rules on Time Scales

Monotonicity rules for the quotient of two functions play foundational roles in the fields of mathematics and applied mathematics. In this paper, we establish monotonicity rules for the L’Hospital type, the quotient of two Laplace transforms, and the quotient of two variable limit integrals with del...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 47; no. 1
Main Authors Mao, Zhong-Xuan, Tian, Jing-Feng
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.01.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Hospitals
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Quotients
Time
26E70
Monotonicity rule
Time scale
L’Hospital
26A48
Laplace transform
Delta derivative
Variable limit integrals
Delta integral
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Summary:Monotonicity rules for the quotient of two functions play foundational roles in the fields of mathematics and applied mathematics. In this paper, we establish monotonicity rules for the L’Hospital type, the quotient of two Laplace transforms, and the quotient of two variable limit integrals with delta derivatives and delta integrals on time scales. Some generalized forms for these monotonicity rules are also considered in detail. As an application, we utilize monotonicity rules to demonstrate that a function is strictly decreasing.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01599-8