References
- A. Abdeldaim and M. Yakout., On some new integral inequalities of Gronwall-Bellman-Pachpatte type, Appl. Math. Comut., 217(2011) 7887-7899. https://doi.org/10.1016/j.amc.2011.02.093
- D. Bainov and P. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers, New York, 1992.
- V. Barbu, Differential Equations, (in Romanian), Ed. Junimca, Iasi, 1985.
- R. Bellman and L. K. Kooke, Differential-Difference Equations, Acad. Press, New York, 1963.
- R. Bellman, Stability Theory of Differential Equations, McGraw Hill, New York, 1953.
- R. Bellman, The stability of solutions of linear differential equations, Duke Math. J., 10(1943), 643-647. https://doi.org/10.1215/S0012-7094-43-01059-2
- H. El-Owaidy, A. A. Ragab, and A. Abdeldaim, On some integral inequalities of Gronwall-Bellman type, Appl. Math. Comut., 106(1999), 289-303. https://doi.org/10.1016/S0096-3003(98)10131-5
- H. T. Gronwall, Note on the derivatives with respect to a parameter of the solutions of differential equations, Ann. of Math., 20(2)(1919), 292-296. https://doi.org/10.2307/1967124
- G. H. Hardy, J. E. Littlewood, G. Polya, Iequalities, second ed, Cambridg Univ. Press, London New York, 1952. 41(3)(2004), 559-571.
- B. G. Pachpatte, A note on Gronwall-Bellman inequality, J. Math. Anal. Appl., 44(1973), 758-762. https://doi.org/10.1016/0022-247X(73)90014-0
- B. G. Pachpatte, Inqualities for Differntial and Integral Equations, Academic Press, New York and London, 1998.
- D. Willett, W. S. J. Wong, On the discrete analogues of some generalization of Gronwall's inequality, Monatsh 69(1965), 362-367. https://doi.org/10.1007/BF01297622
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