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

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Abstract

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.

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Authors and Affiliations

  1. Hebei Key Laboratory of Physics and Energy Technology, Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding, 071003, People’s Republic of China

    Zhong-Xuan Mao & Jing-Feng Tian

  2. School of Mathematics, Jilin University, Qianjin Street 2699, Changchun, 130012, People’s Republic of China

    Zhong-Xuan Mao

Authors
  1. Zhong-Xuan Mao
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  2. Jing-Feng Tian
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Correspondence to Jing-Feng Tian.

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Communicated by Rosihan M. Ali.

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Mao, ZX., Tian, JF. Delta L’Hospital-, Laplace- and Variable Limit-Type Monotonicity Rules on Time Scales. Bull. Malays. Math. Sci. Soc. 47, 1 (2024). https://doi.org/10.1007/s40840-023-01599-8

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  • DOI: https://doi.org/10.1007/s40840-023-01599-8

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