Integral Inequalities of Gronwall-Bellman Type

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References

[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.