On some new integral inequalities for functions in one and two variables

Acta Mathematica Sinica, English Series

Volumn 21, Issue 2, 2005, Pages 423-434

  Kim, Young Ho ^a  

^a Changwon National University   (South Korea)

Author keywords

Bernoulli's inequality; Hyperbolic partial delay differential equation; Integral inequality; Two independent variables

Indexed keywords

EID: 17444421950     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-004-0463-7     Document Type: Article

References (14)

1. Gronwall, T. H.: Note on the derivatives with respect to a parameter of solutions of a system of differential equations. Ann. Math., 20, 292-296 (1919)
2. Bellman, R.: The stability of solutions of linear differential equations. Duke Math. J., 10, 643-647 (1943)
3. Bihari, I.: A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations. Acta. Math. Acad. Sci. Hungar., 7, 81-94 (1965)
4. Lipovan, O.: A retarded Gronwall-like inequality and its applications. J. Math. Anal. Appl., 252, 389-401 (2000)
5. Medved, M.: Nonlinear singular integral inequalities for functions in two and n independent variables. J. Inequalities and Appl., 5, 287-308 (2000)
6. Bainov, D., Simeonov, P.: Integral Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1992
7. Beckenbach, E. F., Bellman, R.: Inequalities, Springer-Verlag, New York, 1961
8. Constantin, A.: Monotone iterative technique for a nonlinear integral equation. J. Math. Anal. Appl., 205, 280-283 (1997)
9. Dragomir, S. S.: On Gronwall type lemmas and applications, "Monografii Matematics" Univ. Timişoara No. 29, 1987
10. Dragomir, S. S., Ionescu, N. M.: On nonlinear integral inequalities in two independent variables. Studia Univ. Babeş-Bolyai, Math., 34, 11-17 (1989)
11. Mitrinović, D. S., Pečarić, J. E., Fink, A. M.: Classical and new Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, Boston, London, 1993
12. Pachpatte, B. G.: Inequalities for Differential and Integral Equations, Academic Press, New York, 1998
13. Pachpatte, B. G.: On some new inequalities related to a certain inequality arising in the theory of differential equations. J. Math. Anal. Appl, 251, 736-751 (2000)
14. Pachpatte, B. G.: Explicit bounds on certain integral inequalities. J. Math. Anal. Appl., 267, 48-61 (2002)