Bazı sabit nokta yineleme yöntemlerinin yakınsama davranışlarının incelenmesi

Abstract

Bazı sabit nokta yineleme yöntemlerinin, belirli bir büzülme şartını sağlayan operatörlerin sınıfından seçilen
elemanların karakterlerine bağlı olarak farklı yakınsama davranışları sergiledikleri nümerik bir örnek verilerek
gösterilecektir.

Keywords

• konveks ve hiperbolik metrik uzaylar,yakınsaklık,yineleme metotları

Investigation of convergency behaviors of some fixed point iteration methods

Abstract

It will be shown by providing a numerical example that some fixed point iteration methods exhibit different
convergency behaviors depending on the characters of the members chosen from a class of operators satisfying a
certain contractive condition.

Keywords

• convex and hyperbolic metric spaces,convergence,iteration methods

References

1. Berinde, V. (2004). Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators. Fixed Point Theory Appl., 97-105.
2. Chugh, R., Preety, M., & Kumar, V. (2015). On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces. Journal of Function Spaces, 2015, 1-11.
3. Ćirić, L., Rafiq, A., Radenović, S., Rajović, M., & Ume, J. S. (2008). On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings,”. Applied Mathematics and Computation, 198(1), 128–137.
4. Doğan, K., & Karakaya, V. (2014). On the Convergence and Stability Results for a New General Iterative Process. The Scientific World Journal, 1-8.
5. Gürsoy, F. (2016). A Picard-S iterative method for approximating fixed point of weak-contraction mappings. Filomat, 30(10), 2829-2845.
6. Gürsoy, F., Khan, A. R., & Fukhar-ud-din, H. (2016). Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics, 1-16.
7. Imoru, C. O., & Olatinwo, M. O. (2003). On the stability of Picard and Mann iteration processes. Carpathian Journal of Mathematics, 19(2), 155–160.
8. Ishikawa, S. (1974). Fixed points by a new iteration method. Proc. Amer. Math. Soc., 44, 147-150.

9. Karakaya, V., Gürsoy, F., & Ertürk, M. (2016). Some convergence and data dependence results for various fixed point iterative methods. Kuwait Journal of Science, 43(1), 112-128.
10. Khan, A. R., Khamsi, M. A., & Fukhar-ud-din, h. (2011). Strong convergence of a general iteration scheme in CAT(0)−spaces. Nonlinear Anal., 74(3), 783–791.
11. Kirk, W. A. (1981). Krasnoselskii’s iteration process in hyperbolic space. Numer. Funct. Anal. Optim., 4(4), 371–381.
12. Kohlenbach, U. (2005). Some logical metatheorems with applications in functional analysis. Trans. Amer. Math. Soc., 357(1), 89-128.
13. Mann, W. (1953). Mean value methods in iteration. Proc. Amer. Math. Soc., 4, 506-510.
14. Noor, M. A. (2000). New approximation schemes for general variational inequalities. J. Math. Anal. Appl., 251(1), 217-229.
15. Phuengrattana, W., & Suantai, S. (2013). Comparison of the rate of convergence of various iterative methods for the class of weak contractions in Banach spaces. Thai J. Math., 217-226.
16. Şahin, A., & Başarır, M. (2016). Convergence and data dependence results of an iteration process in a hyperbolic space. Filomat, 30(3), 569–582.
17. Takahashi, W. (1970). A convexity in metric spaces and nonexpansive mappings I. Kodai Math. Sem. Rep., 22(2), 142-149.