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

PDF
  • Vahid Darvish1,
  • Sever Silvestru Dragomir2,
  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

Published in Issue 2025-11-09

How to Cite

Convergence of general composite iterative method for infinite family of nonexpansive mappings in Hilbert spaces. (2025). Communications in Nonlinear Analysis, 1(1). https://oiccpress.com/cna/article/view/17830

PDF views: 180

Abstract

In this paper by using W_n -mapping, we introduce a composite iterative method for finding a commonfixed 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 rightsreserved.

Keywords

  • Nonexpansive mapping,
  • W_n -mapping
PDF

References

  1. [1] V. Darvish, S. M. Vaezpour, Strong convergence of a new composite iterative method for equilibrium problemsand fixed point problems in Hilbert spaces, J. Adv. Math. Appl., 3 (2014), 148–157.
  2. [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. [3] A. Kangtunyakarn, S. Suantai, A new mapping for finding common solutions of equilibrium problems and fixedpoint problems of finite family of nonexpansive mappings, Nonlinear Anal., 71 (2009), 4448–4460.
  4. [4] T. H. Kim, H. K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal., 61 (2009), 51–60.
  5. [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. [6] K. Shimoji, W. Takahashi, Strong convergence to common fixed points of infinite nonexpansive mappings andapplications, Taiwanese J. Math, 5 (2001), 387–404.
  7. [7] U. Singthong, S. Suantai, A new general iteartive method for a finite family of nonexpansive mappings in Hilbertspaces, Fixed Point Theory Appl., 2010 (2010), 12 pages.
  8. [8] R. Wangkeeree, U.Kamraska, A general iterative method for solving the variational inequality problem and fixedpoint problem of an infinite family of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2009(2009), 23 pages.