Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 957363, 11 pages
http://dx.doi.org/10.1155/2013/957363
Research Article

General Iterative Methods for System of Equilibrium Problems and Constrained Convex Minimization Problem in Hilbert Spaces

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

Received 29 December 2012; Accepted 12 July 2013

Academic Editor: Luigi Muglia

Copyright © 2013 Peichao Duan. 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. 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 Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Y. Liu, “A general iterative method for equilibrium problems and strict pseudo-contractions in Hilbert spaces,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 10, pp. 4852–4861, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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 · View at MathSciNet
  4. 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 A, vol. 69, no. 3, pp. 1025–1033, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. V. Colao, G. L. Acedo, and G. Marino, “An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 7-8, pp. 2708–2715, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. Duan, “Convergence theorems concerning hybrid methods for strict pseudocontractions and systems of equilibrium problems,” Journal of Inequalities and Applications, vol. 2010, Article ID 396080, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. He, S. Liu, and Y. J. Cho, “An explicit method for systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings,” Journal of Computational and Applied Mathematics, vol. 235, no. 14, pp. 4128–4139, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L.-C. Ceng, Q. H. Ansari, and J.-C. Yao, “Some iterative methods for finding fixed points and for solving constrained convex minimization problems,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 74, no. 16, pp. 5286–5302, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Tian and L. Liu, “General iterative methods for equilibrium and constrained convex minimization problem,” Optimazation, 2012. View at Publisher · View at Google Scholar
  10. 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 · View at MathSciNet
  11. 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 Zentralblatt MATH · View at MathSciNet
  12. M. Su and H.-K. Xu, “Remarks on the gradient-projection algorithm,” Journal of Nonlinear Analysis and Optimization, vol. 1, no. 1, pp. 35–43, 2010. View at Google Scholar · View at MathSciNet
  13. S. Wang, “A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces,” Applied Mathematics Letters of Rapid Publication, vol. 24, no. 6, pp. 901–907, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  14. 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 · View at MathSciNet