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Abstract and Applied Analysis
Volume 2014, Article ID 539701, 9 pages
http://dx.doi.org/10.1155/2014/539701
Research Article

New Explicit Bounds on Gamidov Type Integral Inequalities for Functions in Two Variables and Their Applications

1School of Science, Southwest University of Science and Technology, Mianyang 621010, China
2School of Business, Sichuan University, Chengdu 610064, China

Received 14 February 2014; Accepted 10 June 2014; Published 22 June 2014

Academic Editor: Praveen Agarwal

Copyright © 2014 Kelong Cheng and Chunxiang Guo. 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.

Linked References

  1. W.-S. Cheung and Q.-H. Ma, “On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications,” Journal of Inequalities and Applications, no. 4, pp. 347–361, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Deng and C. Prather, “Generalization of an impulsive nonlinear singular Gronwall-Bihari inequality with delay,” Journal of Inequalities in Pure and Applied Mathematics, vol. 9, no. 2, article 34, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. Deng, “Nonlinear discrete inequalities with two variables and their applications,” Applied Mathematics and Computation, vol. 217, no. 5, pp. 2217–2225, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. S. Dragomir and Y.-H. Kim, “Some integral inequalities for functions of two variables,” Electronic Journal of Differential Equations, vol. 2003, article 10, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. S. Dragomir, Some Gronwall type inequalities and Applications, Nova Science Publishers, New York, NY, USA, 2003. View at Zentralblatt MATH · View at MathSciNet
  6. S. G. Gamidov, “Integral inequalities for boundary value problems for differential equations,” Differential Equations, vol. 5, pp. 463–472, 1969. View at Google Scholar · View at MathSciNet
  7. Y.-H. Kim, “Gronwall, Bellman and Pachpatte type integral inequalities with applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 12, pp. e2641–e2656, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Medveď, “Nonlinear singular integral inequalities for functions in two and n independent variables,” Journal of Inequalities and Applications, vol. 5, no. 3, pp. 287–308, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. Tian, M. Fan, and F. Meng, “A generalization of retarded integral inequalities in two independent variables and their applications,” Applied Mathematics and Computation, vol. 221, pp. 239–248, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W.-S. Wang, “A generalized retarded Gronwall-like inequality in two variables and applications to BVP,” Applied Mathematics and Computation, vol. 191, no. 1, pp. 144–154, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W.-S. Wang and C.-X. Shen, “On a generalized retarded integral inequality with two variables,” Journal of Inequalities and Applications, vol. 2008, Article ID 518646, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. Zhang and F. Meng, “On certain integral inequalities in two independent variables for retarded equations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 608–616, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K. Zheng, “Some retarded nonlinear integral inequalities in two variables and applications,” Journal of Inequalities in Pure and Applied Mathematics, vol. 9, no. 2, article 57, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. K. Zheng, “Bounds on some new weakly singular Wendroff-type integral inequalities and applications,” Journal of Inequalities and Applications, vol. 2013, article 159, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. Bainov and P. Simeonov, Integral Inequalities and Applications, vol. 57 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  16. B. G. Pachpatte, “A note on certain integral inequality,” Tamkang Journal of Mathematics, vol. 33, no. 4, pp. 353–358, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. B. G. Pachpatte, “Explicit bounds on Gamidov type integral inequalities,” Tamkang Journal of Mathematics, vol. 37, no. 1, pp. 1–9, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. B. G. Pachpatte, “On a certain retarded integral inequality and its applications,” Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 1, article 19, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Q.-H. Ma and J. Pečarić, “On certain new nonlinear retarded integral inequalities for functions in two variables and their applications,” Journal of the Korean Mathematical Society, vol. 45, no. 1, pp. 121–136, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. F. C. Jiang and F. W. Meng, “Explicit bounds on some new nonlinear integral inequalities with delay,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 479–486, 2007. View at Publisher · View at Google Scholar · View at MathSciNet