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Journal of Applied Mathematics
Volume 2012, Article ID 341953, 11 pages
http://dx.doi.org/10.1155/2012/341953
Research Article

An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings

School of Mathematics and Information Engineering, Taizhou University, Linhai 317000, China

Received 4 September 2011; Accepted 16 September 2011

Academic Editor: Yonghong Yao

Copyright © 2012 Youli Yu. 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. S. Chang, “On the convergence problems of Ishikawa and Mann iterative processes with error for Φ-pseudo contractive type mappings,” Applied Mathematics and Mechanics, vol. 21, no. 1, pp. 1–12, 2000. View at Publisher · View at Google Scholar
  2. C. E. Chidume and C. Moore, “The solution by iteration of nonlinear equations in uniformly smooth Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 215, no. 1, pp. 132–146, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Q. H. Liu, “The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings,” Journal of Mathematical Analysis and Applications, vol. 148, no. 1, pp. 55–62, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, pp. 506–510, 1953. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. M. O. Osilike, “Iterative solution of nonlinear equations of the Φ-strongly accretive type,” Journal of Mathematical Analysis and Applications, vol. 200, no. 2, pp. 259–271, 1996. View at Publisher · View at Google Scholar
  6. S. Reich, “Iterative methods for accretive sets,” in Nonlinear Equations in Abstract Spaces, pp. 317–326, Academic Press, New York, NY, USA, 1978. View at Google Scholar · View at Zentralblatt MATH
  7. Y. Yao, G. Marino, and Y. C. Liou, “A hybrid method for monotone variational inequalities involving pseudocontractions,” Fixed Point Theory and Applications, vol. 2011, Article ID 180534, 8 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. Yao, Y. C. Liou, and S. M. Kang, “Iterative methods for k-strict pseudo-contractive mappings in Hilbert spaces,” Analele Stiintifice ale Universitatii Ovidius Constanta, vol. 19, no. 1, pp. 313–330, 2011. View at Google Scholar
  9. Y. Yao, Y. C. Liou, and J.-C. Yao, “New relaxed hybrid-extragradient method for fixed point problems, a general system of variational inequality problems and generalized mixed equilibrium problems,” Optimization, vol. 60, no. 3, pp. 395–412, 2011. View at Publisher · View at Google Scholar
  10. Y. Yao, Y. J. Cho, and Y. C. Liou, “Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems,” European Journal of Operational Research, vol. 212, no. 2, pp. 242–250, 2011. View at Publisher · View at Google Scholar
  11. S. Ishikawa, “Fixed points and iteration of a nonexpansive mapping in a Banach space,” Proceedings of the American Mathematical Society, vol. 59, no. 1, pp. 65–71, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. C. E. Chidume and S. A. Mutangadura, “An example of 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
  13. C. E. Chidume and H. Zegeye, “Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps,” Proceedings of the American Mathematical Society, vol. 132, no. 3, pp. 831–840, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. N. Shioji and W. Takahashi, “Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces,” Proceedings of the American Mathematical Society, vol. 125, no. 12, pp. 3641–3645, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. C. H. Morales and J. S. Jung, “Convergence of paths for pseudocontractive mappings in Banach spaces,” Proceedings of the American Mathematical Society, vol. 128, no. 11, pp. 3411–3419, 2000. View at Publisher · View at Google Scholar
  16. S. S. Chang, Y. J. Cho, and H. Zhou, Iterative Methods for Nonlinear Operator Equations in Banach Spaces, Nova Science, Huntington, NY, USA, 2002.
  17. T. H. Kim and H. K. Xu, “Strong convergence of modified Mann iterations,” Nonlinear Analysis, Theory, Methods & Applications, vol. 61, no. 1-2, pp. 51–60, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung, and S. M. Kang, “Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 224, no. 1, pp. 149–165, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH