Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 47 Sayı: 3, 615 - 623, 01.06.2018

Öz

Kaynakça

  • 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

Yıl 2018, Cilt: 47 Sayı: 3, 615 - 623, 01.06.2018

Öz

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.

Kaynakça

  • 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Rahim Shah

Akbar Zada

Yayımlanma Tarihi 1 Haziran 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 47 Sayı: 3

Kaynak Göster

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. Haziran 2018;47(3):615-623.
Chicago Shah, Rahim, ve Akbar Zada. “A Fixed Point Approach to the Stability of a Nonlinear Volterra Integrodifferential Equation With Delay”. Hacettepe Journal of Mathematics and Statistics 47, sy. 3 (Haziran 2018): 615-23.
EndNote Shah R, Zada A (01 Haziran 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 ve A. Zada, “A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay”, Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 3, ss. 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 (Haziran 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 ve Akbar Zada. “A Fixed Point Approach to the Stability of a Nonlinear Volterra Integrodifferential Equation With Delay”. Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 3, 2018, ss. 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.