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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 902437, 12 pages
http://dx.doi.org/10.1155/2012/902437
Research Article

Approximation of Common Fixed Points of a Sequence of Nearly Nonexpansive Mappings and Solutions of Variational Inequality Problems

1Department of Mathematics, Banaras Hindu University, Varanasi 221005, India
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 10 April 2012; Accepted 14 May 2012

Academic Editor: Yonghong Yao

Copyright © 2012 D. R. Sahu 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. R. P. Agarwal, D. O'Regan, and D. R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, Topological Fixed Point Theory and Its Applications, Springer, New York, NY, USA, 2009.
  2. D. R. Sahu, “Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces,” Commentationes Mathematicae Universitatis Carolinae, vol. 46, no. 4, pp. 653–666, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. 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 Google Scholar · View at Scopus
  4. 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 Scopus
  5. 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 Scopus
  6. Y. Liu, “A general iterative method for equilibrium problems and strict pseudo-contractions in Hilbert spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 10, pp. 4852–4861, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. 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 and Applications, vol. 70, no. 3, pp. 1257–1264, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Wang, “Convergence and weaker control conditions for hybrid iterative algorithms,” Fixed Point Theory and Applications, vol. 2011, no. 1, article 3, 14 pages, 2011. View at Publisher · View at Google Scholar
  9. S. Wang, “Two general algorithms for computing fixed points of nonexpansive mappings in Banach spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 658905, 11 pages, 2012. View at Google Scholar
  10. S. Wang and C. Hu, “Two new iterative methods for a countable family of nonexpansive mappings in Hilbert spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 852030, 12 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Tian, “A general iterative algorithm for nonexpansive mappings in Hilbert spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 73, no. 3, pp. 689–694, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. 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 (Haifa, 2000), D. Butnariu, Y. Censor, and S. Reich, Eds., vol. 8, pp. 473–504, Studies in Computational Mathematics, Amsterdam, The Netherlands, 2001. View at Google Scholar
  13. 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 and Applications, vol. 74, no. 16, pp. 5286–5302, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. K. Aoyama, Y. Kimura, W. Takahashi, and M. Toyoda, “Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space,” Nonlinear Analysis, Theory, Methods and Applications, vol. 67, no. 8, pp. 2350–2360, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. N. C. Wong, D. R. Sahu, and J. C. Yao, “A generalized hybrid steepest-descent method for variational inequalities in Banach spaces,” Fixed Point Theory and Applications, vol. 2011, Article ID 754702, 28 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. K. Goebel and W. A. Kirk, Topics on Metric Fixed Point Theory, Cambridge University Press, Cambridge, UK, 1990.
  17. 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 Scopus
  18. N. C. Wong, D. R. Sahu, and J. C. Yao, “Solving variational inequalities involving nonexpansive type mappings,” Nonlinear Analysis, Theory, Methods and Applications, vol. 69, no. 12, pp. 4732–4753, 2008. View at Publisher · View at Google Scholar · View at Scopus