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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5129051, 10 pages
Research Article

A Generalization of Linear and Nonlinear Retarded Integral Inequalities in Two Independent Variables

School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China

Correspondence should be addressed to Guojing Xing

Received 26 August 2017; Accepted 5 December 2017; Published 25 December 2017

Academic Editor: Eric R. Kaufmann

Copyright © 2017 Ying Jiang et al. 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.


Integral inequalities, which provide explicit bounds on unknown functions, are used to serve as handy tools in the study of the qualitative properties of solutions to differential and integral equations. By utilizing some analysis techniques, such as amplification method, differential, and integration, several new types of linear and nonlinear retarded integral inequalities in two independent variables are provided. These results generalize and complement previous ones. An illustrative example is given to support the obtained results. The study of the numerical example shows that the new results presented in this paper work well in the analysis of retarded integral inequalities in two independent variables.