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On Some New Nonlinear Integral Inequalities of Gronwall-Bellman Type

El-Owaidy, Hassan Mostafa;Ragab, Abdelwahab Abbas;Eldeeb, Ahmed Abdel-Moneim;Abuelela, Waleed Mostafa Kamal

  • Received : 2012.12.28
  • Accepted : 2013.04.15
  • Published : 2014.12.23

Abstract

In this paper, we establish some new nonlinear integral inequalities of Gronwall-Bellman type. These inequalities generalize some famous inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some nonlinear ordinary differential and integral equations. More accurately we extend certain results which have been proved in A. Abdeldaim and M. Yakout [1] and H. El-Owaidy, A. A. Ragab, A. Abdeldaim [7] too.

Keywords

Gronwall-Bellman inequality;integral inequalities;ordinary differential equations;integral equations

References

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Cited by

  1. On generalized of certain retarded nonlinear integral inequalities and its applications in retarded integro-differential equations vol.256, 2015, https://doi.org/10.1016/j.amc.2015.01.047
  2. On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation vol.23, pp.3, 2015, https://doi.org/10.1016/j.joems.2014.12.001
  3. On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations vol.25, pp.3, 2017, https://doi.org/10.1016/j.joems.2017.02.001