Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2009, Article ID 391839, 9 pages
http://dx.doi.org/10.1155/2009/391839
Research Article

A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

Received 16 December 2008; Accepted 9 April 2009

Academic Editor: Jie Xiao

Copyright © 2009 Suwicha Imnang 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. G. Liu, D. Lei, and S. Li, “Approximating fixed points of nonexpansive mappings,” International Journal of Mathematics and Mathematical Sciences, vol. 24, no. 3, pp. 173–177, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. W. A. Kirk, “On successive approximations for nonexpansive mappings in Banach spaces,” Glasgow Mathematical Journal, vol. 12, no. 1, pp. 6–9, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Maiti and B. Saha, “Approximating fixed points of nonexpansive and generalized nonexpansive mappings,” International Journal of Mathematics and Mathematical Sciences, vol. 16, no. 1, pp. 81–86, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. F. Senter and W. G. Dotson Jr., “Approximating fixed points of nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 44, no. 2, pp. 375–380, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. Das and J. P. Debata, “Fixed points of quasinonexpansive mappings,” Indian Journal of Pure and Applied Mathematics, vol. 17, no. 11, pp. 1263–1269, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. W. Takahashi and T. Tamura, “Convergence theorems for a pair of nonexpansive mappings,” Journal of Convex Analysis, vol. 5, no. 1, pp. 45–56, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z. Opial, “Weak convergence of the sequence of successive approximations for nonexpansive mappings,” Bulletin of the American Mathematical Society, vol. 73, no. 4, pp. 591–597, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. E. Chidume and N. Shahzad, “Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings,” Nonlinear Analysis, vol. 62, no. 6A, pp. 1149–1156, 2005. View at Google Scholar · View at Zentralblatt MATH
  9. H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Y. J. Cho, H. Zhou, and G. Guo, “Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings,” Computers & Mathematics with Applications, vol. 47, no. 4-5, pp. 707–717, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. Suantai, “Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 506–517, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet