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New Integral Inequalities for Iterated Integrals with Applications
Journal of Inequalities and Applications volume 2007, Article number: 024385 (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.
References
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.2004.04.067
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.2005.08.009
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.2005.347
Pachpatte BG: Inequalities for Differential and Integral Equations, Mathematics in Science and Engineering. Volume 197. Academic Press, San Diego, Calif, USA; 1998:x+611.
Pachpatte BG: Explicit bounds on certain integral inequalities. Journal of Mathematical Analysis and Applications 2002,267(1):48–61. 10.1006/jmaa.2001.7743
Pachpatte BG: On some retarded integral inequalities and applications. Journal of Inequalities in Pure and Applied Mathematics 2002,3(2, article 18):1–7.
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.
Pachpatte BG: Inequalities applicable to certain partial differential equations. Journal of Inequalities in Pure and Applied Mathematics 2004,5(2, article 27):1–12.
Pachpatte BG: On some new nonlinear retarded integral inequalities. Journal of Inequalities in Pure and Applied Mathematics 2004,5(3, article 80):1–8.
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.2006.05.061
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.
Baĭnov D, Simeonov P: Integral Inequalities and Applications, Mathematics and Its Applications. Volume 57. Kluwer Academic, Dordrecht, The Netherlands; 1992:xii+245.
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.
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.
Dragomir SS, Kim Y-H: Some integral inequalities for functions of two variables. Electronic Journal of Differential Equations 2003, (10):1–13.
Kim B-I: On some Gronwall type inequalities for a system integral equation. Bulletin of the Korean Mathematical Society 2005,42(4):789–805.
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)00409-8
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.2008.45.1.121
Yang-Liang LO: The boundedness of solutions of linear differential equations. Advances in Mathematics 1957, 3: 409–415.
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Agarwal, R.P., Ryoo, C.S. & Kim, YH. New Integral Inequalities for Iterated Integrals with Applications. J Inequal Appl 2007, 024385 (2008). https://doi.org/10.1155/2007/24385
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DOI: https://doi.org/10.1155/2007/24385