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  • Research Article
  • Open Access

New Integral Inequalities for Iterated Integrals with Applications

Journal of Inequalities and Applications20082007:024385

https://doi.org/10.1155/2007/24385

  • Received: 20 September 2007
  • Accepted: 15 November 2007
  • Published:

Abstract

Some new nonlinear retarded integral inequalities of Gronwall type are established. These inequalities can be used as basic tools in the study of certain classes of integrodifferential equations.

Keywords

  • Basic Tool
  • Integral Inequality
  • Integrodifferential Equation
  • Iterate Integral
  • Gronwall Type

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901-6975, USA
(2)
Department of Mathematics, Hannam University, Daejeon, 306-791, South Korea
(3)
Department of Applied Mathematics, Changwon National University, Changwon, Kyungnam, 641-773, South Korea

References

  1. Agarwal RP, Deng S, Zhang W: Generalization of a retarded Gronwall-like inequality and its applications. Applied Mathematics and Computation 2005,165(3):599–612. 10.1016/j.amc.2004.04.067MathSciNetView ArticleMATHGoogle Scholar
  2. Cheung WS: Some new nonlinear inequalities and applications to boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 2006,64(9):2112–2128. 10.1016/j.na.2005.08.009MathSciNetView ArticleMATHGoogle Scholar
  3. Cheung WS, Ma QH: On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications. Journal of Inequalities and Applications 2005,2005(4):347–361. 10.1155/JIA.2005.347MathSciNetView ArticleMATHGoogle Scholar
  4. Pachpatte BG: Inequalities for Differential and Integral Equations, Mathematics in Science and Engineering. Volume 197. Academic Press, San Diego, Calif, USA; 1998:x+611.Google Scholar
  5. Pachpatte BG: Explicit bounds on certain integral inequalities. Journal of Mathematical Analysis and Applications 2002,267(1):48–61. 10.1006/jmaa.2001.7743MathSciNetView ArticleMATHGoogle Scholar
  6. Pachpatte BG: On some retarded integral inequalities and applications. Journal of Inequalities in Pure and Applied Mathematics 2002,3(2, article 18):1–7.Google Scholar
  7. Pachpatte BG: On a certain retarded integral inequality and applications. Journal of Inequalities in Pure and Applied Mathematics 2004,5(1, article 19):1–9.Google Scholar
  8. Pachpatte BG: Inequalities applicable to certain partial differential equations. Journal of Inequalities in Pure and Applied Mathematics 2004,5(2, article 27):1–12.Google Scholar
  9. Pachpatte BG: On some new nonlinear retarded integral inequalities. Journal of Inequalities in Pure and Applied Mathematics 2004,5(3, article 80):1–8.Google Scholar
  10. Ye H, Gao J, Ding Y: A generalized Gronwall inequality and its application to a fractional differential equation. Journal of Mathematical Analysis and Applications 2007,328(2):1075–1081. 10.1016/j.jmaa.2006.05.061MathSciNetView ArticleMATHGoogle Scholar
  11. Zhao X, Meng F: On some advanced integral inequalities and their applications. Journal of Inequalities in Pure and Applied Mathematics 2005,6(3, article 60):8 pages.MathSciNetGoogle Scholar
  12. Baĭnov D, Simeonov P: Integral Inequalities and Applications, Mathematics and Its Applications. Volume 57. Kluwer Academic, Dordrecht, The Netherlands; 1992:xii+245.View ArticleGoogle Scholar
  13. Cho YJ, Dragomir SS, Kim Y-H: On some integral inequalities with iterated integrals. Journal of the Korean Mathematical Society 2006,43(3):563–578.MathSciNetView ArticleMATHGoogle Scholar
  14. Dragomir SS, Kim Y-H: On certain new integral inequalities and their applications. Journal of Inequalities in Pure and Applied Mathematics 2002,3(4, article 65):1–8.MathSciNetGoogle Scholar
  15. Dragomir SS, Kim Y-H: Some integral inequalities for functions of two variables. Electronic Journal of Differential Equations 2003, (10):1–13.Google Scholar
  16. Kim B-I: On some Gronwall type inequalities for a system integral equation. Bulletin of the Korean Mathematical Society 2005,42(4):789–805.MathSciNetView ArticleMATHGoogle Scholar
  17. Lipovan O: A retarded integral inequality and its applications. Journal of Mathematical Analysis and Applications 2003,285(2):436–443. 10.1016/S0022-247X(03)00409-8MathSciNetView ArticleMATHGoogle Scholar
  18. Ma Q-H, Pečarić J: On certtain new nonlinear retared integral inequalities for functions in two variables and their applications, . Journal of The Korean Mathematical Society 2008,45(1):121–136. 10.4134/JKMS.2008.45.1.121MathSciNetView ArticleMATHGoogle Scholar
  19. Yang-Liang LO: The boundedness of solutions of linear differential equations. Advances in Mathematics 1957, 3: 409–415.MathSciNetGoogle Scholar

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