ON SOME INTEGRAL INEQUALITIES WITH ITERATED INTEGRALS

- Journal title : Journal of the Korean Mathematical Society
- Volume 43, Issue 3, 2006, pp.563-578
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2006.43.3.563

Title & Authors

ON SOME INTEGRAL INEQUALITIES WITH ITERATED INTEGRALS

Cho, Yeol-Je; Dragomir Sever-S.; Kim, Young-Ho;

Cho, Yeol-Je; Dragomir Sever-S.; Kim, Young-Ho;

Abstract

The main aim of the present paper is to establish some new Gronwall type inequalities involving iterated integrals and give some applications of the main results.

Keywords

Gronwall-Bellman inequalities;integral inequality;interated integrals;nondecreasing function;

Language

English

Cited by

1.

ON SOME NEW NONLINEAR RETARDED INTEGRAL INEQUALITIES WITH ITERATED INTEGRALS AND THEIR APPLICATIONS,Ma, Qing-Hua;Pecaric, Josip;

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References

1.

D. Bainov and P. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1992

2.

E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, New York, 1961

3.

R. Bellman, The stability of solutions of linear differential equations, Duke Math. J. 10 (1943), 643-647

4.

I. Bihari, A generalization of a lemma of Bellman and its application to unique- ness problems of differential equations, Acta. Math. Acad. Sci. Hungar. 7 (1956), 81-94

5.

Ya. V. Bykov and Kh. M. Salpagarov, On the theory of integro-differential equations, in Investigations in Integro-Differential Equations in Khirghizia 2 Izd. Akad. Nauk Kirghizia SSR, (1962) (in Russian)

6.

S. S. Dragomir and N. M. Ionescu, On nonlinear integral inequalities in two independent variables, Studia Univ. Babes-Bolyai, Math. 34 (1989), no. 2, 11- 17

7.

S. S. Dragomir and Y. -H. Kim, On certain new integral inequalities and their applications, JIPAM. J. Inequal. Pure Appl. Math. 3 (2002), 1-8, Issue 4, Article 65

8.

S. S. Dragomir and Y. -H. Kim, Some integral inequalities for function of two variables, Electron. J. Differential Equations 10 (2003), 1-13

9.

T. H. Gronwall, Note on the derivatives with respect to a parameter of solutions of a system of differential equations, Ann. of Math. 20 (1919), no. 4, 292-296

10.

L. Guiliano, Generalazzioni di un lemma di Gronwall, Rend. Accad., Lincei, 1946, pp. 1264-1271

11.

C. E. Langenhop, Bounds on the norm of a solution of a general differential equation, Proc. Amer. Math. Soc. 11 (1960), 795-799

12.

A. Mate and P. Neval, Sublinear perturbations of the differential equation $y^{(n)}=0$ and of the analogous difference equation, J. Differential Equations 53 (1984), no. 2, 234-257

13.

D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, Boston, London, 1991

14.

V. V. Nemyckii and V. V. Stepanov, Qualitative theory of differential equations (Russian), Moscow, OGIZ, 1947

15.

B. G. Pachpatte, On some fundamental integral inequalities and their discrete analogues, J. Inequal. Pure Appl. Math. 2 (2001), 1-13, Issue 2, Article 15

16.

M. Rab, Linear integral inequalities, Arch. Math. (Brno) 15 (1979), no. 1, 37-46

17.

Yu. A. Ved, On perturbations of linear homogeneous differential equations with variable coefficients, In: Issled. Integro-Differents. Uravn. Kirghizia 3 Ilim. Frunze (1965), (In Russian)