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Some Nonlinear Integral Inequalities on Time Scales

Abstract

The purpose of this paper is to investigate some nonlinear integral inequalities on time scales. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. The theoretical results are illustrated by a simple example at the end of this paper.

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References

  1. 1.

    Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Agarwal R, Bohner M, Peterson A: Inequalities on time scales: a survey. Mathematical Inequalities & Applications 2001,4(4):535–557.

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Akin-Bohner E, Bohner M, Akin F: Pachpatte inequalities on time scales. Journal of Inequalities in Pure Applied Mathematics 2005,6(1, article 6):23 pages.

    MathSciNet  Google Scholar 

  4. 4.

    Bohner M, Peterson A: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358.

    Google Scholar 

  5. 5.

    Bohner M, Peterson A: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348.

    Google Scholar 

  6. 6.

    Li WN: Some new dynamic inequalities on time scales. Journal of Mathematical Analysis and Applications 2006,319(2):802–814. 10.1016/j.jmaa.2005.06.065

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Pachpatte DB: Explicit estimates on integral inequalities with time scale. Journal of Inequalities in Pure Applied Mathematics 2006,7(4, article 143):8 pages.

    Google Scholar 

  8. 8.

    Wong F-H, Yeh C-C, Hong C-H: Gronwall inequalities on time scales. Mathematical Inequalities & Applications 2006,9(1):75–86.

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Pachpatte BG: On some new inequalities related to a certain inequality arising in the theory of differential equations. Journal of Mathematical Analysis and Applications 2000,251(2):736–751. 10.1006/jmaa.2000.7044

    MathSciNet  Article  MATH  Google Scholar 

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Correspondence to Wei Nian Li.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Li, W.N., Sheng, W. Some Nonlinear Integral Inequalities on Time Scales. J Inequal Appl 2007, 070465 (2007). https://doi.org/10.1155/2007/70465

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Keywords

  • Theoretical Result
  • Integral Inequality
  • Discrete Analogue
  • Continuous Inequality
  • Nonlinear Integral Inequality
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