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Khan, Z. (2014) Integral Inequalities of Gronwall-Bellman Type. Applied Mathematics, 5, 3484-3488. doi: 10.4236/am.2014.521326.
[1] |
Abdeldaim, A. and Yakout, M.
(2011) On Some New Integral Inequalities of Gronwall-Bellman-Pachpatte
Type. Applied Mathematics and Computation, 217, 7887-7899. http://dx.doi.org/10.1016/j.amc.2011.02.093 |
[2] | Pachpatte, B.G. (2001) On Some Fundamental Integral Inequalities and Their Discrete Analogues. Journal of Inequalities in Pure and Applied Mathematics, 2, Article 15. |
[3] | Pachpatte, B.G. (1994) On Some Fundamental Integral Inequalities Arising in the Theory of Differential Equations. Chinese Journal of Mathematics, 22, 261-273. |
[4] | Pachpatte, B.G. (1996) Comparison Theorems Related to a Certain Inequality Used in the Theory of Differential Equations. Soochow Journal of Mathematics, 22, 383-394. |
[5] | Langenhop, C.E. (1960) Bounds on the Norm of a Solution of a General Differential Equation. Proceedings of the American Mathematical Society, 11, 795-799. |
[6] | Bainov, D. and Simeonov, P. (1992) Integral Inequalities and Applications. Kluwer Academic Publishers, Dordrecht. |
[7] | Mitrinovíc, D.S., Pecaríc, J.E. and Fink, A.M. (1991) Inequalities Involving Functions and Their Integrals and Derivatives. Kluwer Academic Publishers, Dordrecht. |
[8] |
Beckenbach, E.F. and Bellman, R. (1961) Inequalities. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-3-642-64971-4 |
[9] |
Bihari, I. (1956) A
Generalization of a Lemma of Bellman and Its Application to Uniqueness
Problem of Differential Equations. Acta Mathematica Academiae
Scientiarum Hungarica, 7, 71-94. http://dx.doi.org/10.1007/BF02022967 |
[10] | Guiliano, L. (1946) Generalazzioni di un lemma di Gronwall. Rend. Accad., Lincei, 1264-1271. |
[11] |
Bellman, R. (1943) The Stability
of Solutions of Linear Di?erential Equations. Duke Mathematical
Journal, 10, 643- 647. http://dx.doi.org/10.1215/S0012-7094-43-01059-2 |
[12] | Dragomir, S.S. and Kim, Y.H. (2002) On Certain New Integral Inequalities and Their Applications. JIPAM, 3, Article 65. |
[13] | Dragomir, S.S. and Kim, Y.H. (2003) Some Integral Inequalities for Functions of Two Variables. Electronic Journal of Differential Equations, 10, 1-13. |
[14] |
Gronwall, T.H. (1919) Note on
the Derivatives with Respect to a Parameter of Solutions of a System of
Differential Equations. Annals of Mathematics, 20, 292-296. http://dx.doi.org/10.2307/1967124 |
[15] | Nemyckii, V.V. and Stepanov, V.V. (1947) Qualitative Theory of Differential Equations. OGIZ, Moscow. eww141216lx |
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