## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014 (2014), Article ID 359280, 14 pages.

### Generalized Nonlinear Volterra-Fredholm Type Integral Inequality with Two Variables

Yusong Lu, Wu-Sheng Wang, Xiaoliang Zhou, and Yong Huang

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#### Abstract

We establish a class of new nonlinear retarded Volterra-Fredholm type integral inequalities, with two variables, where known function $w$ in integral functions in Q.-H. Ma and J. Pečarić, 2008 is changed into the functions ${w}_{1},{w}_{2}$. By adopting novel analysis techniques, such as change of variable, amplification method, differential and integration, inverse function, and the dialectical relationship between constants and variables, the upper bounds of the embedded unknown functions are estimated. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.

#### Article information

**Source**

J. Appl. Math., Volume 2014 (2014), Article ID 359280, 14 pages.

**Dates**

First available in Project Euclid: 2 March 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1425305702

**Digital Object Identifier**

doi:10.1155/2014/359280

**Mathematical Reviews number (MathSciNet)**

MR3200840

#### Citation

Lu, Yusong; Wang, Wu-Sheng; Zhou, Xiaoliang; Huang, Yong. Generalized Nonlinear Volterra-Fredholm Type Integral Inequality with Two Variables. J. Appl. Math. 2014 (2014), Article ID 359280, 14 pages. doi:10.1155/2014/359280. https://projecteuclid.org/euclid.jam/1425305702

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