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**On some new integral inequalities of Gronwall-Bellman-Pachpatte type.**
*(English)*
Zbl 1220.26012

Summary: We establish new nonlinear integral inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear ordinary differential and integral equations. The purpose of this paper is to extend certain results which were proved by B. G. Pachpatte in [Inequalities for differential and integral equations. San Diego, CA: Academic Press (1998; Zbl 1032.26008)]. Some applications are also given to illustrate the usefulness of our results.

### MSC:

26D15 | Inequalities for sums, series and integrals |

### Keywords:

Gronwall-Bellman inequality; ordinary differential equations; integral equations; integro-differential equations### Citations:

Zbl 1032.26008
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\textit{A. Abdeldaim} and \textit{M. Yakout}, Appl. Math. Comput. 217, No. 20, 7887--7899 (2011; Zbl 1220.26012)

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### References:

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