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.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Burton, T.A.: Volterra Integral and Differential Equations, 2nd ed., Elsevier, Amsterdam (2005).
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).
Corduneanu, C.: Principles of Differential and Integral Equations, 2nd ed., Chelsea, New York (1988).
Forti, G.-L.: Hyers–Ulam stability of functional equations in several variables. Aequationes Math., 50, 143–190 (1995).
Gripenberg, G., Londen, S.-O., Staffans, O.: Volterra Integral and Functional Equations, Cambridge University Press, London (1990).
Hyers, D.H.: On the stability of linear functional equation. Proc. Natl. Acad. Sci. USA, 27, 222–224 (1941).
Hyers, D.H., Isac, G., Rassias, T.M.: Stability of Functional Equations in Several Variables, Birkhäuser, Boston, MA (1998).
Jung, S.M.: Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, FL (2001).
Jung, S.M.: A fixed point approach to the stability of a Volterra integral equation. Fixed Point Theory Appl., article ID 57064 (2007).
Lakshmikantham, V., Rao, M.R.M.: Theory of Integro-differential Equations, Gordon and Breach, Philadelphia, PA (1995).
Rassias, T.M.: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc., 72, 297–300 (1978).
Ulam, S.M.: A Collection of Mathematical Problems, Interscience, New York (1960).
Ulam, S.M.: Sets, Numbers, and Universes. Part III, MIT Press, Cambridge, MA (1974).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-0-8176-4899-2_9
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4898-5
Online ISBN: 978-0-8176-4899-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)