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Journal of Applied Mathematics
Volume 2014, Article ID 327943, 9 pages
http://dx.doi.org/10.1155/2014/327943
Research Article

A Multiple Iterated Integral Inequality and Applications

School of Mathematics and Statistics, Hechi University, Guangxi, Yizhou 546300, China

Received 11 June 2014; Accepted 10 July 2014; Published 22 July 2014

Academic Editor: Daoyi Xu

Copyright © 2014 Zongyi Hou and Wu-Sheng Wang. 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.

Abstract

We establish new multiple iterated Volterra-Fredholm type integral inequalities, where the composite function of the unknown function with nonlinear function in integral functions in [Ma, QH, Pečarić, J: Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities. Nonlinear Anal. 69 (2008) 393–407] is changed into the composite functions of the unknown function with different nonlinear functions , respectively. By adopting novel analysis techniques, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.