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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 791209, 8 pages
http://dx.doi.org/10.1155/2014/791209
Research Article

Viscosity Projection Algorithms for Pseudocontractive Mappings in Hilbert Spaces

1School of Science, Tianjin Polytechnic University, Tianjin 300387, China
2College of Management and Economics, Tianjin University, Tianjin 300072, China
3Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
4Department of Mathematics, Dong-A University, Busan 614-714, Republic of Korea

Received 6 December 2013; Accepted 28 December 2013; Published 9 February 2014

Academic Editor: Chong Li

Copyright © 2014 Xiujuan Pan 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. K. Deimling, “Zeros of accretive operators,” Manuscripta Mathematica, vol. 13, no. 4, pp. 365–374, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. S. Ishikawa, “Fixed points by a new iteration method,” Proceedings of the American Mathematical Society, vol. 44, pp. 147–150, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. C. E. Chidume and S. A. Mutangadura, “An example on the mann iteration method for lipschitz pseudocontractions,” Proceedings of the American Mathematical Society, vol. 129, no. 8, pp. 2359–2363, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. H. Zhou, “Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 343, no. 1, pp. 546–556, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. Y. Yao, Y.-C. Liou, and G. Marino, “A hybrid algorithm for pseudo-contractive mappings,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 10, pp. 4997–5002, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. H. Zegeye, N. Shahzad, and M. A. Alghamdi, “Convergence of Ishikawa's iteration method for pseudocontractive mappings,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 18, pp. 7304–7311, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. L.-C. Ceng, A. Petruşel, and J.-C. Yao, “Strong convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudocontractive mappings,” Applied Mathematics and Computation, vol. 209, no. 2, pp. 162–176, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. L.-C. Ceng, A. Petruşel, and J.-C. Yao, “Iterative approximation of fixed points for asymptotically strict pseudocontractive type mappings in the intermediate sense,” Taiwanese Journal of Mathematics, vol. 15, no. 2, pp. 587–606, 2011. View at Zentralblatt MATH · View at Scopus
  9. L.-C. Ceng and J.-C. Yao, “Strong convergence theorems for variational inequalities and fixed point problems of asymptotically strict pseudocontractive mappings in the intermediate sense,” Acta Applicandae Mathematicae, vol. 115, no. 2, pp. 167–191, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. J. C. Yao and L. C. Zeng, “Strong convergence of averaged approximants for asymptotically pseudocontractive mappings in Banach spaces,” Journal of Nonlinear and Convex Analysis, vol. 8, pp. 451–462, 2007.
  11. L. C. Ceng, Q. H. Ansari, and C. F. Wen, “Implicit relaxed and hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense,” Abstract and Applied Analysis, vol. 2013, Article ID 854297, 14 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. C. E. Chidume, M. Abbas, and B. Ali, “Convergence of the Mann iteration algorithm for a class of pseudocontractive mappings,” Applied Mathematics and Computation, vol. 194, no. 1, pp. 1–6, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. C. E. Chidume and H. Zegeye, “Iterative solution of nonlinear equations of accretive and pseudocontractive types,” Journal of Mathematical Analysis and Applications, vol. 282, no. 2, pp. 756–765, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. L. Ćirić, A. Rafiq, N. Cakić, and J. S. Ume, “Implicit Mann fixed point iterations for pseudo-contractive mappings,” Applied Mathematics Letters, vol. 22, no. 4, pp. 581–584, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. C. Moore and B. V. C. Nnoli, “Strong convergence of averaged approximants for Lipschitz pseudocontractive maps,” Journal of Mathematical Analysis and Applications, vol. 260, no. 1, pp. 269–278, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. A. Udomene, “Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudocontractions in Banach spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 67, no. 8, pp. 2403–2414, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Zegeye, N. Shahzad, and T. Mekonen, “Viscosity approximation methods for pseudocontractive mappings in Banach spaces,” Applied Mathematics and Computation, vol. 185, no. 1, pp. 538–546, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. Q.-B. Zhang and C.-Z. Cheng, “Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space,” Mathematical and Computer Modelling, vol. 48, no. 3-4, pp. 480–485, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. H. Zhou, “Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 70, no. 11, pp. 4039–4046, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. K. Geobel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28, Cambridge Studies in Advanced Mathematics, Cambridge University Press, 1990.
  21. X. Lu, H.-K. Xu, and X. Yin, “Hybrid methods for a class of monotone variational inequalities,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 3-4, pp. 1032–1041, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. H. K. Xu, “Iterative algorithms for nonlinear operators,” Journal of the London Mathematical Society, vol. 2, pp. 1–17, 2002.