Skip to main content
SpringerLink
Log in

Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay

  • Chapter
  • First Online:
Integral Methods in Science and Engineering, Volume 1

Abstract

Considerable attention has been given to the study of the Hyers–Ulam and Hyers–Ulam–Rassias stability of functional equations (see, e.g., [HIR98, Ju01]). The concept of stability for a functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the equation. Thus, the stability question of functional equations is how do the solutions of the inequality differ from those of the given functional equation?

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Burton, T.A.: Volterra Integral and Differential Equations, 2nd ed., Elsevier, Amsterdam (2005).

    MATH  Google Scholar 

  2. Castro, L.P., Ramos, A.: Hyers–Ulam–Rassias stability for a class of nonlinear Volterra integral equations. Banach J. Math. Anal., 3, No. 1, 36–43 (2009).

    MathSciNet  Google Scholar 

  3. Corduneanu, C.: Principles of Differential and Integral Equations, 2nd ed., Chelsea, New York (1988).

    Google Scholar 

  4. Forti, G.-L.: Hyers–Ulam stability of functional equations in several variables. Aequationes Math., 50, 143–190 (1995).

    MATH  MathSciNet  Google Scholar 

  5. Gripenberg, G., Londen, S.-O., Staffans, O.: Volterra Integral and Functional Equations, Cambridge University Press, London (1990).

    MATH  Google Scholar 

  6. Hyers, D.H.: On the stability of linear functional equation. Proc. Natl. Acad. Sci. USA, 27, 222–224 (1941).

    Article  MathSciNet  Google Scholar 

  7. Hyers, D.H., Isac, G., Rassias, T.M.: Stability of Functional Equations in Several Variables, Birkhäuser, Boston, MA (1998).

    MATH  Google Scholar 

  8. Jung, S.M.: Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, FL (2001).

    MATH  Google Scholar 

  9. Jung, S.M.: A fixed point approach to the stability of a Volterra integral equation. Fixed Point Theory Appl., article ID 57064 (2007).

    Google Scholar 

  10. Lakshmikantham, V., Rao, M.R.M.: Theory of Integro-differential Equations, Gordon and Breach, Philadelphia, PA (1995).

    MATH  Google Scholar 

  11. Rassias, T.M.: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc., 72, 297–300 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  12. Ulam, S.M.: A Collection of Mathematical Problems, Interscience, New York (1960).

    MATH  Google Scholar 

  13. Ulam, S.M.: Sets, Numbers, and Universes. Part III, MIT Press, Cambridge, MA (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidade de Aveiro, Aveiro, Portugal

    L. P. Castro & A. Ramos

Authors
  1. L. P. Castro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. P. Castro .

Editor information

Editors and Affiliations

  1. Department of Mathematical , University of Tulsa, South Tucker Drive 800, Tulsa, 74104, U.S.A.

    Christian Constanda

  2. Departamento de Matematica Aplicada, Universidad Cantabria, Santander, 39005, Spain

    M.E. Pérez

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Castro, L.P., Ramos, A. (2010). Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay. In: Constanda, C., Pérez, M. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4899-2_9

Download citation

Publish with us

Policies and ethics

Search

Navigation