Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 987595, 15 pages
http://dx.doi.org/10.5402/2011/987595
Research Article

On Some Nonlinear Integrodifferential Inequalities for Functions of 𝑛 Independent Variables

Department of Mathematics, Faculty of Exact Sciences, University of Mentouri, Constantine 25000, Algeria

Received 23 December 2010; Accepted 11 January 2011

Academic Editors: R. Avery, S. S. Ravindran, and R. Spigler

Copyright © 2011 Hassane Khellaf and Mohamed El-Hadi Smakdji. 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. D. Baĭnov and P. Simeonov, Integral Inequalities and Applications, vol. 57 of Mathematics and Its Applications (East European Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992. View at Zentralblatt MATH
  2. M. Denche and H. Khellaf, “Integral inequalities similar to Gronwall inequality,” Electronic Journal of Differential Equations, vol. 2007, no. 176, pp. 1–14, 2007. View at Google Scholar · View at Zentralblatt MATH
  3. T. H. Gronwall, “Note on the derivatives with respect to a parameter of the solutions of a system of differential equations,” Annals of Mathematics, vol. 20, no. 4, pp. 292–296, 1919. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. B. G. Pachpatte, “On some fundamental integrodifferential and integral inequalities,” Analele Ştiintifice ale Universităţii “Al.I.Cuza” din Iaşi, vol. 23, no. 1, pp. 77–86, 1977. View at Google Scholar · View at Zentralblatt MATH
  5. D. R. Snow, “Gronwall's inequality for systems of partial differential equations in two independent variables,” Proceedings of the American Mathematical Society, vol. 33, pp. 46–54, 1972. View at Google Scholar · View at Zentralblatt MATH
  6. J. A. Oguntuase, “On an inequality of Gronwall,” Journal of Inequalities in Pure and Applied Mathematics, vol. 2, no. 1, article 9, pp. 1–6, 2001. View at Google Scholar · View at Zentralblatt MATH
  7. B. G. Pachpatte, “Bounds on certain integral inequalities,” Journal of Inequalities in Pure and Applied Mathematics, vol. 3, no. 3, article 47, pp. 1–10, 2002. View at Google Scholar · View at Zentralblatt MATH
  8. C. C. Yeh, “On some integral inequalities in n independent variables and their applications,” Journal of Mathematical Analysis and Applications, vol. 86, no. 2, pp. 387–410, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. C. C. Yeh and M. H. Shih, “The Gronwall-Bellman inequality in several variables,” Journal of Mathematical Analysis and Applications, vol. 86, no. 1, pp. 157–167, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. B. G. Pachpatte, “On some new integro-differential inequalities of the Wendroff type,” Journal of Mathematical Analysis and Applications, vol. 73, no. 2, pp. 491–500, 1980. View at Publisher · View at Google Scholar
  11. H. Khellaf, “On integral inequalities for functions of several independent variables,” Electronic Journal of Differential Equations, vol. 2003, no. 123, pp. 1–12, 2003. View at Google Scholar · View at Zentralblatt MATH