Bazı sabit nokta yineleme yöntemlerinin yakınsama davranışlarının incelenmesi

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.

Investigation of convergency behaviors of some fixed point iteration methods

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. *

PDF

___

W. Takahashi, "A convexity in metric spaces and nonexpansive mappings I," Kodai Math. Sem. Rep., vol. 22, no. 2, pp. 142-149, 1970.
H. Fukhar-ud-din and V. Berinde, "Iterative methods for the class of quasi-contractive type operators and comparsion of their rate of convergence in convex metric spaces," Filomat, vol. 30, no. 1, pp. 223-230, 2016.
U. Kohlenbach, "Some logical metatheorems with applications in functional analysis," Trans. Amer. Math. Soc., vol. 357, no. 1, pp. 89-128, 2005.
W. A. Kirk, "Krasnoselskii’s iteration process in hyperbolic space," Numer. Funct. Anal. Optim., vol. 4, no. 4, pp. 371–381, 1981.
A. R. Khan, M. A. Khamsi, and H. Fukhar-ud-din, "Strong convergence of a general iteration scheme in CAT(0)−spaces," Nonlinear Anal., vol. 74, no. 3, pp. 783–791, 2011.
A. Şahin and M. Başarır, "Convergence and data dependence results of an iteration process in a hyperbolic space," Filomat, vol. 30, no. 3, pp. 569– 582, 2016.
R. Chugh, M. Preety, and V. Kumar, "On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces," Journal of Function Spaces, vol. 2015, pp. 1-11, 2015.
F. Gürsoy, "A Picard-S iterative method for approximating fixed point of weak-contraction mappings," Filomat, vol. 30, pp. 2829–2845, 2016.
F. Gürsoy, A. R. Khan, and H. Fukhar-ud-din, "Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces," vol. Doi: 10.15672/HJMS.20174720334, pp. 1-16, 2017.
V. Karakaya, F. Gürsoy, and M. Ertürk, "Some convergence and data dependence results for various fixed point iterative methods," Kuwait Journal of Science, vol. 43, no. 1, pp. 112-128, 2016.
K. Doğan and V. Karakaya, "On the Convergence and Stability Results for a New General Iterative Process," The Scientific World Journal, pp. 1-8, 2014.
W.R. Mann, "Mean value methods in iteration," Proc. Amer. Math. Soc., vol. 4, pp. 506-510, 1953.
S. Ishikawa, "Fixed points by a new iteration method," Proc. Amer. Math. Soc., vol. 44, pp. 147- 150, 1974.
M. A. Noor, "New approximation schemes for general variational inequalities," J. Math. Anal. Appl., vol. 251, no. 1, pp. 217-229, 2000.
L. Ćirić, A. Rafiq, S. Radenović, M. Rajović, and J. S. Ume, "On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings,”," Applied Mathematics and Computation, vol. 198, no. 1, pp. 128–137, 2008.
C. O. Imoru and M. O. Olatinwo, "On the stability of Picard and Mann iteration processes," Carpathian Journal of Mathematics, vol. 19, no. 2, pp. 155–160, 2003.
V. Berinde, "Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators," Fixed Point Theory Appl., pp. 97-105, 2004.
K. Knopp, Infinite sequences and series. New York: Dover Publications, Inc., 1956.
M. Başarır, "On rates of convergence of sequences," J.Orissa Math.Soc., vol. 7, no. 2, pp. 89-98, 1988.