Convergence of general composite iterative method for infinite family of nonexpansive mappings in Hilbert spaces

Authors

1 Department of Mathematics and Computer Science, Amirkabir University of Technology, Hafez Ave., P.O. Box 15875-4413, Tehran, Iran.

2 Mathematics, School of Engineering and Science Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia

Abstract

In this paper by using W_n -mapping, we introduce a composite iterative method for finding a common
fixed point for infinite family of nonexpansive mappings and a solution of a certain variational inequality.
Furthermore, the strong convergence of the proposed iterative method is established. Finally, some sim-
ulation examples are presented. Our results improve and extend the previous results. c ⃝2016 All rights
reserved.

Keywords


[1] V. Darvish, S. M. Vaezpour, Strong convergence of a new composite iterative method for equilibrium problems
and fixed point problems in Hilbert spaces, J. Adv. Math. Appl., 3 (2014), 148–157.

[2] Y. Je Cho, X. Qin, Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces, J.
Comput. Appl. Math., 228 (2009), 458–465. 

[3] A. Kangtunyakarn, S. Suantai, A new mapping for finding common solutions of equilibrium problems and fixed
point problems of finite family of nonexpansive mappings, Nonlinear Anal., 71 (2009), 4448–4460. 

[4] T. H. Kim, H. K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal., 61 (2009), 51–60. 

[5] G. Marino, H. K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal.
Appl., 318 (2006), 43–52.

[6] K. Shimoji, W. Takahashi, Strong convergence to common fixed points of infinite nonexpansive mappings and
applications, Taiwanese J. Math, 5 (2001), 387–404. 

[7] U. Singthong, S. Suantai, A new general iteartive method for a finite family of nonexpansive mappings in Hilbert
spaces, Fixed Point Theory Appl., 2010 (2010), 12 pages. 

[8] R. Wangkeeree, U.Kamraska, A general iterative method for solving the variational inequality problem and fixed
point problem of an infinite family of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2009
(2009), 23 pages.