About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 695183, 20 pages
http://dx.doi.org/10.1155/2012/695183
Research Article

The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 5 August 2012; Accepted 12 December 2012

Academic Editor: Abdelaziz Rhandi

Copyright © 2012 Rabian Wangkeeree and Pakkapon Preechasilp. 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. K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972.
  2. A. Aleyner and Y. Censor, “Best approximation to common fixed points of a semigroup of nonexpansive operators,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 137–151, 2005. View at MathSciNet
  3. A. Aleyner and S. Reich, “An explicit construction of sunny nonexpansive retractions in Banach spaces,” Fixed Point Theory and Applications, vol. 2005, no. 3, pp. 295–305, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. H. Zegeye, N. Shahzad, and O. A. Daman, “Strong convergence theorems for a semigroup of asymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2077–2086, 2011. View at Publisher · View at Google Scholar
  5. F. E. Browder, “Convergence of approximants to fixed points of nonexpansive nonlinear mappings in banach spaces,” Archive for Rational Mechanics and Analysis, vol. 24, no. 1, pp. 82–90, 1967. View at Publisher · View at Google Scholar · View at Scopus
  6. C. H. Morales and J. S. Jung, “Convergence of paths for pseudo-contractive mappings in banach spaces,” Proceedings of the American Mathematical Society, vol. 128, no. 11, pp. 3411–3419, 2000. View at Scopus
  7. W. Takahashi and Y. Ueda, “On Reich's strong convergence theorems for resolvents of accretive operators,” Journal of Mathematical Analysis and Applications, vol. 104, no. 2, pp. 546–553, 1984. View at Scopus
  8. S. Reich, “Strong convergence theorems for resolvents of accretive operators in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 75, no. 1, pp. 287–292, 1980. View at Scopus
  9. J. Schu, “Approximation of fixed points of asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 112, no. 1, pp. 143–151, 1991.
  10. T. C. Lim and H. K. Xu, “Fixed point theorems for asymptotically nonexpansive mappings,” Nonlinear Analysis, vol. 22, no. 11, pp. 1345–1355, 1994. View at Scopus
  11. N. Shioji and W. Takahashi, “Strong convergence theorems for asymptotically nonexpansive semigroups in Hilbert spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 34, no. 1, pp. 87–99, 1998. View at Scopus
  12. F. E. Browder, “Convergence theorems for sequences of nonlinear operators in Banach spaces,” Mathematische Zeitschrift, vol. 100, no. 3, pp. 201–225, 1967. View at Publisher · View at Google Scholar · View at Scopus
  13. R. Wangkeeree, N. Petrot, and R. Wangkeeree, “The general iterative methods for nonexpansive mappings in Banach spaces,” Journal of Global Optimization, vol. 51, no. 1, pp. 27–46, 2011. View at Publisher · View at Google Scholar
  14. G. Marino and H. K. Xu, “A general iterative method for nonexpansive mappings in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 318, no. 1, pp. 43–52, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Li, L. Li, and Y. Su, “General iterative methods for a one-parameter nonexpansive semigroup in Hilbert space,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 9, pp. 3065–3071, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Takahashi, Nonlinear Functional Analysis-Fixed Point Theory and Its Applications, Yokohama Publishers, Yokohama, Japan, 2000.
  17. H. K. Xu, “Viscosity approximation methods for nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 298, no. 1, pp. 279–291, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. H. K. Xu, “An iterative approach to quadratic optimization,” Journal of Optimization Theory and Applications, vol. 116, no. 3, pp. 659–678, 2003. View at Publisher · View at Google Scholar · View at Scopus