Skip to main content

Advertisement

Log in

On Some New Integral Inequalities for Functions in One and Two Variables

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

In this paper, we consider a bound on a general version of the integral inequalities for functions and also study the qualitative behavior of the solutions of certain classes of the hyperbolic partial delay differential equations under the integral inequalities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  4. Lipovan, O.: A retarded Gronwall–like inequality and its applications. J. Math. Anal. Appl., 252, 389–401 (2000)

    Article  MathSciNet  Google Scholar 

  5. Medved, M.: Nonlinear singular integral inequalities for functions in two and n independent variables. J. Inequalities and Appl., 5, 287–308 (2000)

    MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  9. Dragomir, S. S.: On Gronwall type lemmas and applications, "Monografii Matematics" Univ. Timi¸soara 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)

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  14. Pachpatte, B. G.: Explicit bounds on certain integral inequalities. J. Math. Anal. Appl., 267, 48–61 (2002)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Young Ho Kim.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, Y.H. On Some New Integral Inequalities for Functions in One and Two Variables. Acta Math Sinica 21, 423–434 (2005). https://doi.org/10.1007/s10114-004-0463-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-004-0463-7

Keywords

MR (2000) Subject Classification

Navigation