Research Article
BibTex RIS Cite
Year 2018, Volume: 47 Issue: 3, 615 - 623, 01.06.2018

Abstract

References

  • M. Akkouchi, Hyers-Ulam-Rassias stability of nonlinear Volterra integral equations via a xed point approach, Acta Univ. Apulensis Math. Inform., 26 (2011), 257266.
  • L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a xed point approach, Grazer Math. Ber., 346 (2004), 4352.
  • L. P. Castro and A. Ramos, Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations, Banach J. Math. Anal., 3 (2009), 3643.
  • L. P. Castro, A. Ramos, Hyers-Ulam and Hyers-Ulam-Rassias stability of Volterra integral equations with delay, Integral methods in science and engineering, Birkhauser Boston, Inc., Boston, MA, 1 (2010), 8594.
  • J. B. Diaz and B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305309.
  • M. Gachpazan and O. Baghani, Hyers-Ulam stability of Volterra integral equation, J. Nonl. Anal. Appl., 1 (2010), 1925.
  • M. Gachpazan and O. Baghani, Hyers-Ulam stability of nonlinear integral equation, Fix. P. Theo. Appl., 2010 (2010), 6 pages.
  • D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A, 27 (1941), 222224.
  • S. M. Jung, A xed point approach to the stability of a Volterra integral equation. Fix. P. Theo. Appl., 2007 (2007), 9 pages.
  • S. M. Jung, A fixed point approach to the stability of differential equations y0 = F (x, y), Bull. Malays. Math. Sci. Soc., 33 (2010), 4756.
  • S. M. Jung, S. Sevgin and H. Sevli, On the perturbation of Volterra integro-differential equations, Appl. Math. Lett., 26 (2013), 665669.
  • J. R. Morales and E. M. Rojas, Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay, Int. J. Nonl. Anal. Appl., 2 (2011), 16.
  • T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297300.
  • J. M. Rassias and M. Eslamian, Fixed points and stability of nonic functional equation in quasi- -normed spaces, Cont. Anal. Appl. Math., 3 (2015), 293309.
  • S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, New York, (1960).
  • A. Zada, R. Shah and T. Li, Integral type contraction and coupled coincidence xed point theorems for two pairs in G-metric spaces, Hacet. J. Math. Stat., 45 (2016), 14751484.

A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay

Year 2018, Volume: 47 Issue: 3, 615 - 623, 01.06.2018

Abstract

By using a fixed point method, we prove the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of a nonlinear Volterra integrodifferential equation with delay. Two examples are presented to support the usability of our results.

References

  • M. Akkouchi, Hyers-Ulam-Rassias stability of nonlinear Volterra integral equations via a xed point approach, Acta Univ. Apulensis Math. Inform., 26 (2011), 257266.
  • L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a xed point approach, Grazer Math. Ber., 346 (2004), 4352.
  • L. P. Castro and A. Ramos, Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations, Banach J. Math. Anal., 3 (2009), 3643.
  • L. P. Castro, A. Ramos, Hyers-Ulam and Hyers-Ulam-Rassias stability of Volterra integral equations with delay, Integral methods in science and engineering, Birkhauser Boston, Inc., Boston, MA, 1 (2010), 8594.
  • J. B. Diaz and B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305309.
  • M. Gachpazan and O. Baghani, Hyers-Ulam stability of Volterra integral equation, J. Nonl. Anal. Appl., 1 (2010), 1925.
  • M. Gachpazan and O. Baghani, Hyers-Ulam stability of nonlinear integral equation, Fix. P. Theo. Appl., 2010 (2010), 6 pages.
  • D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A, 27 (1941), 222224.
  • S. M. Jung, A xed point approach to the stability of a Volterra integral equation. Fix. P. Theo. Appl., 2007 (2007), 9 pages.
  • S. M. Jung, A fixed point approach to the stability of differential equations y0 = F (x, y), Bull. Malays. Math. Sci. Soc., 33 (2010), 4756.
  • S. M. Jung, S. Sevgin and H. Sevli, On the perturbation of Volterra integro-differential equations, Appl. Math. Lett., 26 (2013), 665669.
  • J. R. Morales and E. M. Rojas, Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay, Int. J. Nonl. Anal. Appl., 2 (2011), 16.
  • T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297300.
  • J. M. Rassias and M. Eslamian, Fixed points and stability of nonic functional equation in quasi- -normed spaces, Cont. Anal. Appl. Math., 3 (2015), 293309.
  • S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, New York, (1960).
  • A. Zada, R. Shah and T. Li, Integral type contraction and coupled coincidence xed point theorems for two pairs in G-metric spaces, Hacet. J. Math. Stat., 45 (2016), 14751484.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Rahim Shah

Akbar Zada

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 3

Cite

APA Shah, R., & Zada, A. (2018). A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay. Hacettepe Journal of Mathematics and Statistics, 47(3), 615-623.
AMA Shah R, Zada A. A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay. Hacettepe Journal of Mathematics and Statistics. June 2018;47(3):615-623.
Chicago Shah, Rahim, and Akbar Zada. “A Fixed Point Approach to the Stability of a Nonlinear Volterra Integrodifferential Equation With Delay”. Hacettepe Journal of Mathematics and Statistics 47, no. 3 (June 2018): 615-23.
EndNote Shah R, Zada A (June 1, 2018) A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay. Hacettepe Journal of Mathematics and Statistics 47 3 615–623.
IEEE R. Shah and A. Zada, “A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, pp. 615–623, 2018.
ISNAD Shah, Rahim - Zada, Akbar. “A Fixed Point Approach to the Stability of a Nonlinear Volterra Integrodifferential Equation With Delay”. Hacettepe Journal of Mathematics and Statistics 47/3 (June 2018), 615-623.
JAMA Shah R, Zada A. A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay. Hacettepe Journal of Mathematics and Statistics. 2018;47:615–623.
MLA Shah, Rahim and Akbar Zada. “A Fixed Point Approach to the Stability of a Nonlinear Volterra Integrodifferential Equation With Delay”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, 2018, pp. 615-23.
Vancouver Shah R, Zada A. A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay. Hacettepe Journal of Mathematics and Statistics. 2018;47(3):615-23.