Open Access

New Integral Inequalities for Iterated Integrals with Applications

Journal of Inequalities and Applications20082007:024385

DOI: 10.1155/2007/24385

Received: 20 September 2007

Accepted: 15 November 2007

Published: 6 February 2008

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.

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Florida Institute of Technology
(2)
Department of Mathematics, Hannam University
(3)
Department of Applied Mathematics, Changwon National University

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

Copyright

© Ravi P. Agarwal et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.