On some integral inequalities with iterated integrals

Journal of the Korean Mathematical Society

Volumn 43, Issue 3, 2006, Pages 563-578

  Cho, Yeol Je ^a   Dragomir, Sever S ^b   Kim, Young Ho ^c  

^a Gyeongsang National University   (South Korea)

^b VICTORIA UNIVERSITY   (Australia)

^c Changwon National University   (South Korea)

Author keywords

Gronwall Bellman inequalities; Integral inequality; Iterated integrals; Nondecreasing function

Indexed keywords

EID: 33646519741     PISSN: 03049914     EISSN: None     Source Type: Journal    
DOI: 10.4134/JKMS.2006.43.3.563     Document Type: Conference Paper

References (17)

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 uniqueness 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. lonescu, On nonlinear integral inequalities in two independent variables, Studia Univ. Babeş-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. __, 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. (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. Ráb, 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 Him. Frunze (1965), (In Russian).