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ISRN Applied Mathematics
Volume 2012 (2012), Article ID 576018, 10 pages
http://dx.doi.org/10.5402/2012/576018
Research Article

Convergence of a General Composite Iterative Method for a Countable Family of Nonexpansive Mappings

School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224051 Jiangsu, China

Received 17 March 2012; Accepted 10 May 2012

Academic Editors: A. Bellouquid, E. Kita, and J. Nedoma

Copyright © 2012 Shuang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. S. Jung, “Convergence on composite iterative schemes for nonexpansive mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 167535, 14 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. M. Tian, “A general iterative algorithm for nonexpansive mappings in Hilbert spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 3, pp. 689–694, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. K. Aoyama, Y. Kimura, W. Takahashi, and M. Toyoda, “Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space,” Nonlinear Analysis. Theory, Methods & Applications, vol. 67, no. 8, pp. 2350–2360, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. J. S. Jung, “Strong convergence of composite iterative methods for nonexpansive mappings,” Journal of the Korean Mathematical Society, vol. 46, no. 6, pp. 1151–1164, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. W. Takahashi and K. Shimoji, “Convergence theorems for nonexpansive mappings and feasibility problems,” Mathematical and Computer Modelling, vol. 32, no. 11-13, pp. 1463–1471, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. K. Shimoji and W. Takahashi, “Strong convergence to common fixed points of infinite nonexpansive mappings and applications,” Taiwanese Journal of Mathematics, vol. 5, no. 2, pp. 387–404, 2001. View at Zentralblatt MATH
  7. S.-S. Chang, H. W. Joseph Lee, and C. K. Chan, “A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 9, pp. 3307–3319, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. H. Yao, Y.-C. Liou, and J.-C. Yao, “Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2007, Article ID 64363, 12 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. J.-W. Peng and J.-C. Yao, “A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 12, pp. 6001–6010, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Wang, “A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces,” Applied Mathematics Letters, vol. 24, no. 6, pp. 901–907, 2011. View at Publisher · View at Google Scholar
  11. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, vol. 28, Cambridge University Press, Cambridge, UK, 1990. View at Publisher · View at Google Scholar