Yıl 2018, Cilt 47, Sayı 3, Sayfalar 615 - 623 2018-06-01
| | | |

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

#### Rahim Shah [1] , Akbar Zada [2]

##### 39 127

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.

Hyers-Ulam-Rassias stability, Hyers-Ulam stability, Volterra integrodifferential equation with delay, fixed point approach
• M. Akkouchi, Hyers-Ulam-Rassias stability of nonlinear Volterra integral equations via a xed point approach, Acta Univ. Apulensis Math. Inform., 26 (2011), 257266.
• L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a xed point approach, Grazer Math. Ber., 346 (2004), 4352.
• L. P. Castro and A. Ramos, Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations, Banach J. Math. Anal., 3 (2009), 3643.
• 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), 8594.
• 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), 305309.
• M. Gachpazan and O. Baghani, Hyers-Ulam stability of Volterra integral equation, J. Nonl. Anal. Appl., 1 (2010), 1925.
• 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), 222224.
• 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 differential equations y0 = F (x, y), Bull. Malays. Math. Sci. Soc., 33 (2010), 4756.
• S. M. Jung, S. Sevgin and H. Sevli, On the perturbation of Volterra integro-differential equations, Appl. Math. Lett., 26 (2013), 665669.
• 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), 16.
• T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297300.
• J. M. Rassias and M. Eslamian, Fixed points and stability of nonic functional equation in quasi- -normed spaces, Cont. Anal. Appl. Math., 3 (2015), 293309.
• 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), 14751484.
Birincil Dil en Matematik Matematik Yazar: Rahim Shah Yazar: Akbar Zada
 Bibtex @araştırma makalesi { hujms440356, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {615 - 623}, doi = {}, title = {A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay}, key = {cite}, author = {Shah, Rahim and Zada, Akbar} } 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. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/440356 MLA 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 47 (2018): 615-623 Chicago 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 47 (2018): 615-623 RIS TY - JOUR T1 - A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay AU - Rahim Shah , Akbar Zada Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 615 EP - 623 VL - 47 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay %A Rahim Shah , Akbar Zada %T A fixed point approach to the stability of a nonlinear volterra integrodifferential equation with delay %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 3 %R %U 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.