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Journal of Applied Mathematics
Volume 2013, Article ID 647524, 6 pages
http://dx.doi.org/10.1155/2013/647524
Research Article

An Iterative Method with Norm Convergence for a Class of Generalized Equilibrium Problems

1Department of Mathematics, Henan Normal University, Xinxiang 453007, China
2Department of Mathematics, Luoyang Normal University, Luoyang 471022, China

Received 12 January 2013; Accepted 1 July 2013

Academic Editor: Filomena Cianciaruso

Copyright © 2013 Haixia Zhang and Fenghui Wang. 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. S. Takahashi and W. Takahashi, “Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 3, pp. 1025–1033, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  2. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28, Cambridge University Press, Cambridge, UK, 1990.
  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 MathSciNet
  4. P. L. Combettes, “Solving monotone inclusions via compositions of nonexpansive averaged operators,” Optimization, vol. 53, no. 5-6, pp. 475–504, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  5. H.-K. Xu, “Averaged mappings and the gradient-projection algorithm,” Journal of Optimization Theory and Applications, vol. 150, no. 2, pp. 360–378, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  6. 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 MathSciNet
  7. S. D. Flåm and A. S. Antipin, “Equilibrium programming using proximal-like algorithms,” Mathematical Programming, vol. 78, no. 1, pp. 29–41, 1997. View at Google Scholar · View at MathSciNet
  8. 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 MathSciNet
  9. 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 MathSciNet
  10. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Springer, Dordrecht, The Netherlands, 1996.
  11. J.-B. Baillon and G. Haddad, “Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones,” Israel Journal of Mathematics, vol. 26, no. 2, pp. 137–150, 1977. View at Google Scholar · View at MathSciNet
  12. F. Wang and H.-K. Xu, “Strongly convergent iterative algorithms for solving a class of variational inequalities,” Journal of Nonlinear and Convex Analysis, vol. 11, no. 3, pp. 407–421, 2010. View at Google Scholar · View at MathSciNet