Some New Impulsive Integral Inequalities

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Some new impulsive integral inequalities related to certain integral inequalities are established, which extend the results proved by J. Li in [On some new impulsive integral inequalities, Journal of Inequalities and Applications, Vol. 200. The inequalities given here can be used as basic tools in the qualitative theory of certain impulsive differential and integral equations.

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876-879

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April 2014

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© 2014 Trans Tech Publications Ltd. All Rights Reserved

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[1] V. Lakshmikantham, D. D. Bainov, and P.S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, (1989).

DOI: 10.1142/0906

Google Scholar

[2] D. Bainov and P. Simeonov, Integral Inequalities and Applications, vol. 57 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, (1992).

Google Scholar

[3] P. Y. H. Pang and R. P. Agarwal, On an integral inequality and its discrete analogues, Journal of Mathematical Analysis and Applications, vol. 194, no. 2, pp.569-577, (1995).

DOI: 10.1006/jmaa.1995.1318

Google Scholar

[4] S. S. Dragomir and Y. H. Kim, Some integral inequalities for functions of two variables, Electronic Journal of Differential Equations, no. 10, pp.1-13, (2003).

Google Scholar

[5] B. G. Pachpatte, On some fundamental integral inequalities and their discrete analogues, Journal of Inequalities in Pure and Applied mathematics, vol. 2, no. 2, article 15, 13 pages, (2001).

Google Scholar

[6] B. G. Pachpatte, Integral inequalities of the Bihari type, Mathmatical Inequalities & Applications, vol. 5, no. 4, pp.649-657, (2002).

DOI: 10.7153/mia-05-66

Google Scholar

[7] W. S. Cheung, J. L. Ren, Discrete non-linear inequalities and applications to boundary value problems, Journal of Mathematical Analysis and Applications, vol. 319, no. 1, pp.708-724, (2006).

DOI: 10.1016/j.jmaa.2005.06.064

Google Scholar

[8] W. S. Cheung, Some new nonlinear inequalities and applications to boundary value problems, Nonlinear Analysis: Theory Methods & Applications, vol. 64, no. 9, pp.2112-2128, 200.

DOI: 10.1016/j.na.2005.08.009

Google Scholar

[9] N. –E. Tatar, An impulsive nonlinear singular version of the Gronwall-Bihari inequalitiy, , Journal of Inequalities and Applications, Vol. (2006).

DOI: 10.1155/jia/2006/84561

Google Scholar

[10] X. Liu and Q. Wang, The method of Lyapunov functionals and exponential stability of impulsive systems with time delay, Nonlinear Analysis: Theory Methods & Applications, vol. 66, no. 7, pp.1465-1484, (2007).

DOI: 10.1016/j.na.2006.02.004

Google Scholar

[11] J. Li, On some new impulsive integral inequalities, Journal of Inequalities and Applications, Vol. (2008).

Google Scholar