Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 275826, 15 pages
doi:10.1155/2010/275826
Research Article

Gronwall-OuIang-Type Integral Inequalities on Time Scales

Ailian Liu1,2 and Martin Bohner2

1School of Statistics and Mathematics, Shandong Economic University, Jinan 250014, China
2Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA

Received 20 April 2010; Accepted 3 August 2010

Academic Editor: Wing-Sum Cheung

Copyright © 2010 Ailian Liu and Martin Bohner. 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 present several Gronwall-OuIang-type integral inequalities on time scales. Firstly, an OuIang inequality on time scales is discussed. Then we extend the Gronwall-type inequalities to multiple integrals. Some special cases of our results contain continuous Gronwall-type inequalities and their discrete analogues. Several examples are included to illustrate our results at the end.