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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 517460, 13 pages
http://dx.doi.org/10.1155/2012/517460
Research Article

An Implicit Algorithm for Maximal Monotone Operators and Pseudocontractive Mappings

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
3School of Management, North University for Nationalities, Yinchuan 750021, China
4Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

Received 21 February 2012; Accepted 28 February 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Hong-Jun Li et al. 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. M. A. Noor and K. I. Noor, “Sensitivity analysis for quasi-variational inclusions,” Journal of Mathematical Analysis and Applications, vol. 236, no. 2, pp. 290–299, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. M. A. Noor, “Generalized set-valued variational inclusions and resolvent equations,” Journal of Mathematical Analysis and Applications, vol. 228, no. 1, pp. 206–220, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Y. Yao and J. C. Yao, “On modified iterative method for nonexpansive mappings and monotone mappings,” Applied Mathematics and Computation, vol. 186, no. 2, pp. 1551–1558, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. R. Chen, Y. Su, and H. K. Xu, “Regularization and iteration methods for a class of monotone variational inequalities,” Taiwanese Journal of Mathematics, vol. 13, no. 2B, pp. 739–752, 2009. View at Zentralblatt MATH
  5. Y. P. Fang and N. J. Huang, “H-monotone operator and resolvent operator technique for variational inclusions,” Applied Mathematics and Computation, vol. 145, no. 2-3, pp. 795–803, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. Takahashi, W. Takahashi, and M. Toyoda, “Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces,” Journal of Optimization Theory and Applications, vol. 147, no. 1, pp. 27–41, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Yao and N. Shahzad, “New methods with perturbations for non-expansive mappings in Hilbert spaces,” Fixed Point Theory and Applications, vol. 2011, article 79, 2011. View at Publisher · View at Google Scholar
  8. R. T. Rockafellar, “On the maximal monotonicity of subdifferential mappings,” Pacific Journal of Mathematics, vol. 33, pp. 209–216, 1970. View at Zentralblatt MATH
  9. M. Aslam Noor and T. M. Rassias, “Projection methods for monotone variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 237, no. 2, pp. 405–412, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. A. Noor and Z. Huang, “Some resolvent iterative methods for variational inclusions and nonexpansive mappings,” Applied Mathematics and Computation, vol. 194, no. 1, pp. 267–275, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Y. Yao, Y.-C. Liou, and S. M. Kang, “Two-stepprojection 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 & Computer Modelling, vol. 55, pp. 1506–1515, 2012. View at Publisher · View at Google Scholar
  13. S. Adly, “Perturbed algorithms and sensitivity analysis for a general class of variational inclusions,” Journal of Mathematical Analysis and Applications, vol. 201, no. 2, pp. 609–630, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. G. Marino and H.-K. Xu, “Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 336–349, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. W. Takahashi and M. Toyoda, “Weak convergence theorems for nonexpansive mappings and monotone mappings,” Journal of Optimization Theory and Applications, vol. 118, no. 2, pp. 417–428, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. T. Suzuki, “Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces,” Fixed Point Theory and Applications, vol. 2005, no. 1, pp. 103–123, 2005. View at Zentralblatt MATH
  17. H.-K. Xu, “Iterative algorithms for nonlinear operators,” Journal of the London Mathematical Society. Second Series, vol. 66, no. 1, pp. 240–256, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. K. Aoyama, Y. Kimura, W. Takahashi, and M. Toyoda, “On a strongly nonexpansive sequence in Hilbert spaces,” Journal of Nonlinear and Convex Analysis, vol. 8, no. 3, pp. 471–489, 2007. View at Zentralblatt MATH
  19. E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” The Mathematics Student, vol. 63, no. 1–4, pp. 123–145, 1994. View at Zentralblatt MATH
  20. P. L. Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005. View at Zentralblatt MATH
  21. Y. Yao, Y.-C. Liou, and J.-C. Yao, “An extragradient method for fixed point problems and variational inequality problems,” Journal of Inequalities and Applications, vol. 2007, Article ID 38752, 12 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. Y. Yao, Y.-C. Liou, and Y.-J. Wu, “An extragradient method for mixed equilibrium problems and fixed point problems,” Fixed Point Theory and Applications, vol. 2009, Article ID 632819, 15 pages, 2009. View at Zentralblatt MATH
  23. 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, vol. 2009, Article ID 279058, 7 pages, 2009. View at Zentralblatt MATH
  24. F. Cianciaruso, G. Marino, L. Muglia, and Y. Yao, “On a two-step algorithm for hierarchical fixed point problems and variational inequalities,” Journal of Inequalities and Applications, vol. 2009, Article ID 208692, 13 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH