Abstract and Applied Analysis

Generalizations of Wendroff Integral Inequalities and Their Discrete Analogues

Maksat Ashyraliyev

Full-text: Open access


Generalizations of Wendroff type integral inequalities with four dependent limits and their discrete analogues are obtained. In applications, these results are used to establish the stability estimates for the solution of the Goursat problem.

Article information

Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 768062, 15 pages.

First available in Project Euclid: 5 April 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Ashyraliyev, Maksat. Generalizations of Wendroff Integral Inequalities and Their Discrete Analogues. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 768062, 15 pages. doi:10.1155/2012/768062. https://projecteuclid.org/euclid.aaa/1365174044

Export citation


  • M. Ashyraliyev, “A note on the stability of the integral-differential equation of the hyperbolic type in a Hilbert space,” Numerical Functional Analysis and Optimization, vol. 29, no. 7-8, pp. 750–769, 2008.
  • S. G. Krein, Linear Differential Equations in a Banach Space, Nauka, Moscow, Russia, 1966.
  • R. P. Agarwal, M. Bohner, and V. B. Shakhmurov, “Maximal regular boundary value problems in Banach-valued weighted space,” Boundary Value Problems, no. 1, pp. 9–42, 2005.
  • S. Ashirov and N. Kurbanmamedov, “Investigation of the solution of a class of integral equations of Volterra type,” Izvestiya Vysshikh Uchebnykh Zavedeniĭ Matematika, vol. 9, pp. 3–8, 1987.
  • S. Ashirov and Y. D. Mamedov, “A Volterra-type integral equation,” Ukrainian Mathematical Journal, vol. 40, no. 4, pp. 438–442, 1988.
  • A. Ashyralyev, E. Misirli, and O. Mogol, “A note on the integral inequalities with two dependent limits,” Journal of Inequalities and Applications, vol. 2010, Article ID 430512, 2010.
  • A. Ashyralyev and P. E. Sobolevskii, New Difference Schemes for Partial Differential Equations, Birkhäuser, Berlin, Germany, 2004.
  • A. Ashyralyev and P. E. Sobolevskiĭ, Well-Posedness of Parabolic Difference Equations, Birkhäuser, Berlin, Germany, 1994.
  • P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley & Sons, London, UK, 1962.
  • E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, Germany, 1961.
  • A. Corduneanu, “A note on the Gronwall inequality in two independent variables,” Journal of Integral Equations, vol. 4, no. 3, pp. 271–276, 1982.
  • T. Nurimov and D. Filatov, Integral Inequalities, FAN, Tashkent, Uzbekistan, 1991.