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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 469270, 12 pages
http://dx.doi.org/10.1155/2012/469270
Research Article

Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 18 December 2011; Accepted 3 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Rudong Chen. 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. A. Sabharwal and L. C. Potter, “Convexly constrained linear inverse problems: iterative least-squares and regularization,” IEEE Transactions on Signal Processing, vol. 46, no. 9, pp. 2345–2352, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. Y.-L. Cui and X. Liu, “Notes on Browder's and Halpern's methods for nonexpansive mappings,” Fixed Point Theory, vol. 10, no. 1, pp. 89–98, 2009. View at Zentralblatt MATH
  3. Y. Yao and H.-K. Xu, “Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications,” Optimization, vol. 60, no. 6, pp. 645–658, 2011. View at Publisher · View at Google Scholar
  4. Y. Yao, R. Chen, and H.-K. Xu, “Schemes for finding minimum-norm solutions of variational inequalities,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 7-8, pp. 3447–3456, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. H. H. Bauschke, “The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space,” Journal of Mathematical Analysis and Applications, vol. 202, no. 1, pp. 150–159, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. F. E. Browder, “Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces,” Archive for Rational Mechanics and Analysis, vol. 24, pp. 82–90, 1967.
  7. F. E. Browder and W. V. Petryshyn, “Construction of fixed points of nonlinear mappings in Hilbert space,” Journal of Mathematical Analysis and Applications, vol. 20, pp. 197–228, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. 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 Zentralblatt MATH
  9. S. A. Hirstoaga, “Iterative selection methods for common fixed point problems,” Journal of Mathematical Analysis and Applications, vol. 324, no. 2, pp. 1020–1035, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. P.-E. Mainge, “Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 469–479, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Y. Yao, R. Chen, and J.-C. Yao, “Strong convergence and certain control conditions for modified Mann iteration,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 6, pp. 1687–1693, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. M. Kikkawa and W. Takahashi, “Approximating fixed points of infinite nonexpansive mappings by the hybrid method,” Journal of Optimization Theory and Applications, vol. 117, no. 1, pp. 93–101, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. H. Zegeye and N. Shahzad, “Viscosity approximation methods for a common fixed point of finite family of nonexpansive mappings,” Applied Mathematics and Computation, vol. 191, no. 1, pp. 155–163, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Y. Yao, Y. C. Liou, and G. Marino, “Strong convergence of two iterative algorithms for nonexpansive mappings in Hilbert spaces,” Fixed Point Theory and Applications, Article ID 279058, 7 pages, 2009. View at Zentralblatt MATH
  15. Y. Yao, Y. J. Cho, and Y.-C. Liou, “Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems,” European Journal of Operational Research, vol. 212, no. 2, pp. 242–250, 2011. View at Publisher · View at Google Scholar
  16. S.-S. Chang, “Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1402–1416, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. A. Noor, “Some developments in general variational inequalities,” Applied Mathematics and Computation, vol. 152, no. 1, pp. 199–277, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. M. A. Noor, K. I. Noor, and E. Al-Said, “Iterative methods for solving nonconvex equilibrium variational inequalities,” Applied Mathematics & Information Sciences, vol. 6, no. 1, pp. 65–69, 2012.
  19. M. A. Noor, “Extended general variational inequalities,” Applied Mathematics Letters, vol. 22, no. 2, pp. 182–186, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. M. A. Noor, “Some aspects of extended general variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 303569, 16 pages, 2012.
  21. P. K. F. Kuhfittig, “Common fixed points of nonexpansive mappings by iteration,” Pacific Journal of Mathematics, vol. 97, no. 1, pp. 137–139, 1981. View at Zentralblatt MATH
  22. 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
  23. Y. 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, Article ID 64363, 12 pages, 2007. View at Zentralblatt MATH
  24. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990. View at Publisher · View at Google Scholar
  25. T. Suzuki, “Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces,” Fixed Point Theory and Applications, no. 1, pp. 103–123, 2005. View at Zentralblatt MATH
  26. H.-K. Xu, “Iterative algorithms for nonlinear operators,” Journal of the London Mathematical Society, vol. 66, no. 1, pp. 240–256, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH