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Abstract and Applied Analysis
Volume 2011, Article ID 929037, 18 pages
http://dx.doi.org/10.1155/2011/929037
Research Article

Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 3 February 2011; Accepted 20 June 2011

Academic Editor: Stefan Siegmund

Copyright © 2011 Withun Phuengrattana and Suthep Suantai. 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. B. Halpern, “Fixed points of nonexpanding maps,” Bulletin of the American Mathematical Society, vol. 73, pp. 957–961, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. R. Wittmann, “Approximation of fixed points of nonexpansive mappings,” Archiv der Mathematik, vol. 58, no. 5, pp. 486–491, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. S. Reich, “Approximating fixed points of nonexpansive mappings,” Panamerican Mathematical Journal, vol. 4, no. 2, pp. 23–28, 1994. View at Google Scholar · View at Zentralblatt MATH
  4. N. Shioji and W. Takahashi, “Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces,” Proceedings of the American Mathematical Society, vol. 125, no. 12, pp. 3641–3645, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. T.-H. Kim and H.-K. Xu, “Strong convergence of modified Mann iterations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 61, no. 1-2, pp. 51–60, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. 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
  7. S. Saejung, “Halpern's iteration in CAT(0) spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 471781, 13 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. Cuntavepanit and B. Panyanak, “Strong convergence of modified Halpern iterations in CAT(0) spaces,” Fixed Point Theory and Applications, vol. 2011, Article ID 869458, 11 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. W. Takahashi, “A convexity in metric space and nonexpansive mappings. I,” Kōdai Mathematical Seminar Reports, vol. 22, pp. 142–149, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. K. Aoyama, K. Eshita, and W. Takahashi, “Iteration processes for nonexpansive mappings in convex metric spaces,” in Proceedings of the International Conference on Nonlinear and Convex Analysis, pp. 31–39, 2005.
  11. T. Shimizu and W. Takahashi, “Fixed points of multivalued mappings in certain convex metric spaces,” Topological Methods in Nonlinear Analysis, vol. 8, no. 1, pp. 197–203, 1996. View at Google Scholar · View at Zentralblatt MATH
  12. A. Kaewcharoen and B. Panyanak, “Fixed points for multivalued mappings in uniformly convex metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2008, Article ID 163580, 9 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. F. Bruhat and J. Tits, “Groupes réductifs sur un corps local,” Institut des Hautes Études Scientifiques, no. 41, pp. 5–251, 1972. View at Google Scholar · View at Zentralblatt MATH
  14. S. Dhompongsa and B. Panyanak, “On Δ-convergence theorems in CAT(0) spaces,” Computers & Mathematics with Applications, vol. 56, no. 10, pp. 2572–2579, 2008. View at Publisher · View at Google Scholar
  15. M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, vol. 319, Springer, Berlin, Germany, 1999.
  16. L. Leustean, “A quadratic rate of asymptotic regularity for CAT(0)-spaces,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 386–399, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, Japan, 2000.
  18. T. Shimizu, “A convergence theorem to common fixed points of families of nonexpansive mappings in convex metric spaces,” in Nonlinear Analysis and Convex Analysis, pp. 575–585, Yokohama Publishing, Yokohama, Japan, 2007. View at Google Scholar · View at Zentralblatt MATH
  19. Y. Song and Y. Zheng, “Strong convergence of iteration algorithms for a countable family of nonexpansive mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 7-8, pp. 3072–3082, 2009. View at Publisher · View at Google Scholar
  20. W. Takahashi, “Weak and strong convergence theorems for families of nonexpansive mappings and their applications,” Annales Universitatis Mariae Curie-Skłodowska, vol. 51, no. 2, pp. 277–292, 1997. View at Google Scholar
  21. 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 Google Scholar · View at Zentralblatt MATH
  22. 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