Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 438023, 12 pages
http://dx.doi.org/10.1155/2012/438023
Research Article

Strong Convergence of the Viscosity Approximation Process for the Split Common Fixed-Point Problem of Quasi-Nonexpansive Mappings

College of Science, Civil Aviation University of China, Tianjin 300300, China

Received 14 December 2011; Accepted 11 January 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Jing Zhao and Songnian He. 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. Y. Censor and T. Elfving, “A multiprojection algorithm using Bregman projections in a product space,” Numerical Algorithms, vol. 8, no. 2-4, pp. 221–239, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. C. Byrne, “Iterative oblique projection onto convex sets and the split feasibility problem,” Inverse Problems, vol. 18, no. 2, pp. 441–453, 2002. View at Publisher · View at Google Scholar
  3. C. Byrne, “A unified treatment of some iterative algorithms in signal processing and image reconstruction,” Inverse Problems, vol. 20, no. 1, pp. 103–120, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. P.-E. Maingé, “The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces,” Computers & Mathematics with Applications, vol. 59, no. 1, pp. 74–79, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. B. Qu and N. Xiu, “A note on the CQ algorithm for the split feasibility problem,” Inverse Problems, vol. 21, no. 5, pp. 1655–1665, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. H.-K. Xu, “A variable Krasnosel'skii-Mann algorithm and the multiple-set split feasibility problem,” Inverse Problems, vol. 22, no. 6, pp. 2021–2034, 2006. View at Publisher · View at Google Scholar
  7. Q. Yang, “The relaxed CQ algorithm solving the split feasibility problem,” Inverse Problems, vol. 20, no. 4, pp. 1261–1266, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Q. Yang and J. Zhao, “Generalized KM theorems and their applications,” Inverse Problems, vol. 22, no. 3, pp. 833–844, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Y. Yao, W. Jigang, and Y.-C. Liou, “Regularized methods for the split feasibility problem,” Abstract and Applied Analysis, vol. 2012, Article ID 140679, 13 pages, 2012. View at Publisher · View at Google Scholar
  10. H.-K. Xu, “Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces,” Inverse Problems, vol. 26, no. 10, Article ID 105018, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Y. Yao, Y.-C. Liou, and S. M. Kang, “Two-step projection methods for a system of variational inequality problems in Banach spaces,” Journal of Global Optimization. In press. View at Publisher · View at Google Scholar
  12. Y. Yao, R. Chen, and Y.-C. Liou, “A unified implicit algorithm for solving the triple-hierarchical constrained optimization problem,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 1506–1515, 2012. View at Publisher · View at Google Scholar
  13. Y. Yao, Y.-J. Cho, and Y.-C. Liou, “Hierarchical convergence of an implicit doublenet algorithm for nonexpansive semigroups and variational inequalities,” Fixed Point Theory and Applications, vol. 2011, article 101, 2011. View at Publisher · View at Google Scholar
  14. J. Zhao and Q. Yang, “Several solution methods for the split feasibility problem,” Inverse Problems, vol. 21, no. 5, pp. 1791–1799, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Y. Censor and A. Segal, “The split common fixed point problem for directed operators,” Journal of Convex Analysis, vol. 16, no. 2, pp. 587–600, 2009. View at Google Scholar · View at Zentralblatt MATH
  16. S. Măruşter and C. Popirlan, “On the Mann-type iteration and the convex feasibility problem,” Journal of Computational and Applied Mathematics, vol. 212, no. 2, pp. 390–396, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. A. Moudafi, “A note on the split common fixed-point problem for quasi-nonexpansive operators,” Nonlinear Analysis, vol. 74, no. 12, pp. 4083–4087, 2011. View at Publisher · View at Google Scholar
  18. P.-E. Maingé, “Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization,” Set-Valued Analysis, vol. 16, no. 7-8, pp. 899–912, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH