About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 757986, 6 pages
http://dx.doi.org/10.1155/2013/757986
Research Article

A General Iterative Algorithm with Strongly Positive Operators for Strict Pseudo-Contractions

1Tongji Zhejiang College, Zhejiang 314000, China
2Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, China

Received 6 November 2012; Accepted 2 February 2013

Academic Editor: Claudia Timofte

Copyright © 2013 Wei Xu and Yuanheng 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. A. Moudafi, “Viscosity approximation methods for fixed-points problems,” Journal of Mathematical Analysis and Applications, vol. 241, no. 1, pp. 46–55, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. H.-K. Xu, “Viscosity approximation methods for nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 298, no. 1, pp. 279–291, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Tian, “A general iterative algorithm for nonexpansive mappings in Hilbert spaces,” Nonlinear Analysis: Theory, Methods & Application A, vol. 73, no. 3, pp. 689–694, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. Marino and H.-K. Xu, “A general iterative method for nonexpansive mappings in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 318, no. 1, pp. 43–52, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. F. Deutsch and I. Yamada, “Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings,” Numerical Functional Analysis and Optimization, vol. 19, no. 1-2, pp. 33–56, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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
  7. I. Yamada, “The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, D. Butnariu, Y. Censor, and S. ReichS, Eds., vol. 8, pp. 473–504, North-Holland, Amsterdam, The Netherland, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L.-C. Ceng, S.-M. Guu, and J.-C. Yao, “A general composite iterative algorithm for nonexpansive mappings in Hilbert spaces,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2447–2455, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Y. H. Wang and Y. H. Xia, “Strong convergence for asymptotically pseudo-contractions with the demiclosedness principle in Banach spaces,” Fixed Point Theory and Applications, vol. 2012, article 45, 2012.
  10. Y. L. Song, H. Y. Hu, Y. Q. Wang, et al., “Strong convergence of a new general iterative method for variational inequality problems in Hilbert spaces,” Fixed Point Theory and Applications, vol. 2012, article 46, 2012.
  11. W. Xu and Y. H. Wang, “Strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family strictly non-self pseudo-contractions,” Abstract and Applied Analysis, vol. 2012, Article ID 457024, 11 pages, 2012. View at Publisher · View at Google Scholar
  12. N. Young, An Introduction to Hilbert Space, Cambridge University Press, Cambridge, UK, 1988. View at MathSciNet
  13. Y. H. Yao, M. A. Noor, and Y. C. Liou, “Strong convergence of a modified extragradient method to the miniumnorm solution of variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 817436, 9 pages, 2012. View at Publisher · View at Google Scholar
  14. H. K. Xu and T. H. Kim, “Convergence of hybrid steepest-descent methods for variational inequalities,” Journal of Optimization Theory and Applications, vol. 119, no. 1, pp. 185–201, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. Yao, Y.-C. Liou, and S. M. Kang, “Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3472–3480, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. 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 · View at MathSciNet
  17. Y. Wang and L. Yang, “Modified relaxed extragradient method for a general system of variational inequalities and nonexpansive mappings in Banach spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 818970, 14 pages, 2012. View at Zentralblatt MATH · View at MathSciNet