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Some Difference Inequalities for Iterated Sums with Applications

Author

Listed:
  • Wu-Sheng Wang
  • Shanhe Wu

Abstract

The main objective of this paper is to establish two new nonlinear sum‐difference inequalities with multiple iterated sums. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. These new inequalities can be used as handy tools in the study of the estimation of solutions of difference equations.

Suggested Citation

  • Wu-Sheng Wang & Shanhe Wu, 2013. "Some Difference Inequalities for Iterated Sums with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:804152
    DOI: 10.1155/2013/804152
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    References listed on IDEAS

    as
    1. Hong Zhou & Deqing Huang & Wu-Sheng Wang & Jian-Xin Xu, 2012. "Some New Difference Inequalities and an Application to Discrete‐Time Control Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Zhonghai Guo & Xiaoliang Zhou & Wu-Sheng Wang, 2012. "Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Zhonghai Guo & Xiaoliang Zhou & Wu-Sheng Wang, 2012. "Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-23, June.
    4. Qiuli He & Taixiang Sun & Hongjian Xi, 2013. "Dynamics of a Family of Nonlinear Delay Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-4, May.
    5. Qiuli He & Taixiang Sun & Hongjian Xi, 2013. "Dynamics of a Family of Nonlinear Delay Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Zong-Xuan Chen & Kwang Ho Shon, 2013. "Fixed Points of Meromorphic Solutions for Some Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Zong-Xuan Chen & Kwang Ho Shon, 2013. "Fixed Points of Meromorphic Solutions for Some Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, May.
    8. Hong Zhou & Deqing Huang & Wu-Sheng Wang & Jian-Xin Xu, 2012. "Some New Difference Inequalities and an Application to Discrete-Time Control Systems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, October.
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    Cited by:

    1. Ricai Luo & Wu-Sheng Wang & Honglei Xu, 2014. "Estimation of Unknown Functions of Iterative Difference Inequalities and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Zongyi Hou & Shanhe Wu & Wu-Sheng Wang, 2014. "Some Retarded Difference Inequalities of Product Form and Their Application," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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