Gecikmeli lineer olmayan bir Volterra integral denkleminin çözümü

Year 2017, Volume: 21 Issue: 6, 1367 - 1376, 01.12.2017

Aynur Şahin Zeynep Kalkan Hakan Arısoy

https://doi.org/10.16984/saufenbilder.305632

Cited By: 1

Abstract

Bu makalede, Ullah ve Arshad (SpringerPlus (2016)5:1616)
tarafından tanımlanan iterasyon metodunun basitleştirilmiş hali olan bir iteratif
dizisinin gecikmeli lineer olmayan bir Volterra integral denkleminin çözümüne kuvvetli
yakınsadığı gösterilmiştir. Dahası bu integral denklemin çözümü için bir veri
bağımlılığı sonucu ispatlanmıştır.

Keywords

Volterra integral denklemleri, Sabit nokta, Veri bağımlılığı, iterasyon metotları

On the solution of a nonlinear Volterra integral equation with delay

Abstract

In this paper, we show that the
iterative sequence which is a simplified form of the iteration method
introduced by Ullah and Arshad (SpringerPlus, (2016)5:1616), is
convergent strongly to the solution of a nonlinear Volterra integral equation
with delay in a complete metric space. Furthermore, we prove a data dependence
result for the solution of this integral equation.

Keywords

Volterra integral equations, fixed point, data dependence, iteration methods

References

• L. Cadariu, L. Gavruta and P. Gavruta. (2012). Weighted space method for the stability of some nonlinear equation, Appl. Anal. Discrete Math. 6(1), pp. 126-139.
• L. P. Castro and R. C. Guerra. (2013). Hyers-Ulam-Rassias stability of Volterra integral equations within weighted spaces. Libertas Math. (new series), 33(2), pp. 21-35.
• K. Ullah and M. Arshad. (2016). On different results for the new three step iteration process in Banach spaces. SpringerPlus, 5(1), pp. 1616.
• M. Ertürk, F. Gürsoy, V. Karakaya, M. Başarır and A. Şahin. (2017). Some convergence and data dependence results by a simpler and faster iterative scheme. Appl. Comput. Math. submitted.
• E. M. Picard. (1890). Memorie sur la theorie des equations aux derivees partielles et la methode des approximations successives. J. Math. Pure Appl. 6, pp. 145-210.
• W. R. Mann. (1953). Mean value methods in iterations, Proc. Amer. Math. Soc. 4(3), pp. 506-510.
• S. Ishikawa. (1974). Fixed point by a new iteration method. Proc. Amer. Math. Soc. 41(1), pp. 147-150.
• M. A. Noor. (2000). New approximation schemes for general variational inequalities. J. Math. Anal. Appl. 251, pp. 217-229.
• R. P. Agarwal, D. O'Regan and D.R. Sahu. (2007). Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. 8, pp. 61-79.
• D. R. Sahu. (2011). Applications of S iteration process to constrained minimization problems and split feasibility problems. Fixed Point Theory, 12(1), pp. 187-204.
• R. Chugh, V. Kumar and S. Kumar. (2012). Strong convergence of a new three step iterative scheme in Banach space. Amer. J. Comput. Math. 2, pp. 345-357.
• F. Gürsoy and V. Karakaya. (2014). A Picard-S hybrid type iteration method for solving a differential equation with retarded argument. arXiv:1403.2546v2 [math. FA], https://arxiv.org/abs/1403.2546v2.
• N. Kadıoğlu and I. Yıldırım. (2015) Approximating fixed points of nonexpansive mappings by a faster iteration process. J.Adv. Math. Stud. 8(2), pp. 257-264.
• D. Thakur, B. S. Thakur and M. Postolache. (2014). New iteration schme for numerical reckoning fixed points of nonexpansive mapping. J. Inequal. Appl. 2014:1, 5 pages.
• V. Karakaya, N. E. H. Bouzara, K. Doğan and Y. Atalan. (2015). On different results for a new two-step iteration method under weak-contraction mapping in Banach spaces. arXiv:1507.00200v1 [maths.FA], https://arxiv.org/abs/1507.00200vl.
• M. Abbas and T. Nazır. (2014). A new faster iteration process applied to constrained minimization and feasibility problems. Mat. Vesnik, 66(2), pp. 223-234.
• I. Karahan and M. Özdemir. (2013). A general iterative method for approximation of fixed points and their applications. Adv. Fixed Point Theory, 3(3), pp. 510-526.
• Ş. M. Şoltuz and T. Grosan. (2008). Data dependence for Ishikawa iteration when dealing contractive like ope rators. Fixed Point Theory Appl. 2008: 242916, 7 pages.