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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 276874, 13 pages
http://dx.doi.org/10.1155/2011/276874
Research Article

Strong Convergence Theorems for Equilibrium Problems and 𝑘-Strict Pseudocontractions in Hilbert Spaces

School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received 23 March 2011; Revised 31 May 2011; Accepted 23 June 2011

Academic Editor: Ljubisa Kocinac

Copyright © 2011 Dao-Jun Wen. 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. 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 Google Scholar · View at Zentralblatt MATH
  2. A. Moudafi and M. Théra, “Proximal and dynamical approaches to equilibrium problems,” in Ill-Posed Variational Problems and Regularization Techniques, vol. 477 of Lecture Notes in Economics and Mathematical Systems, pp. 187–201, Springer, Berlin, Germany, 1999. View at Google Scholar · View at Zentralblatt MATH
  3. P. L. Combettes and A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005. View at Google Scholar · View at Zentralblatt MATH
  4. 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. View at Google Scholar
  5. 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
  6. O. Scherzer, “Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems,” Journal of Mathematical Analysis and Applications, vol. 194, no. 3, pp. 911–933, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. M. O. Osilike and D. I. Igbokwe, “Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations,” Computers & Mathematics with Applications, vol. 40, no. 4-5, pp. 559–567, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. 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
  9. 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. 336–346, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. H. Zhou, “Convergence theorems of fixed points for k-strict pseudo-contractions in Hilbert spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 2, pp. 456–462, 2008. View at Publisher · View at Google Scholar
  11. T.-H. Kim and H.-K. Xu, “Strong convergence of modified Mann iterations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 61, no. 1-2, pp. 51–60, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. G. L. Acedo and H.-K. Xu, “Iterative methods for strict pseudo-contractions in Hilbert spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 67, no. 7, pp. 2258–2271, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. Takahashi and W. Takahashi, “Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 331, no. 1, pp. 506–515, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. X. Qin, M. Shang, and S. M. Kang, “Strong convergence theorems of modified Mann iterative process for strict pseudo-contractions in Hilbert spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 3, pp. 1257–1264, 2009. View at Publisher · View at Google Scholar
  15. H. Zhang and Y. Su, “Strong convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 9, pp. 3236–3242, 2009. View at Publisher · View at Google Scholar
  16. L.-C. Ceng, S. Al-Homidan, Q. H. Ansari, and J.-C. Yao, “An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings,” Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 967–974, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. S. Plubtieng and R. Punpaeng, “A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 548–558, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. X. Qin, Y. J. Cho, and S. M. Kang, “Viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 1, pp. 99–112, 2010. View at Publisher · View at Google Scholar
  19. T. Suzuki, “Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals,” Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp. 227–239, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. 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 Zentralblatt MATH