Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 149483, 11 pages
doi:10.1155/2008/149483
Research Article

Strong Convergence of Viscosity Methods for Continuous Pseudocontractions in Banach Spaces

Filomena Cianciaruso,1 Giuseppe Marino,1 Luigi Muglia,1 and Haiyun Zhou2

1Dipartimento di Matematica, Universitá della Calabria, Campus di Arcavacata, Arcavacata di Rende, 87036 Rende, Italy
2Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 13 July 2008; Accepted 15 October 2008

Academic Editor: Hong Kun Xu

Copyright © 2008 Filomena Cianciaruso 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. 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. C. H. Morales, “Strong convergence of path for continuous pseudo-contractive mappings,” Proceedings of the American Mathematical Society, vol. 135, no. 9, pp. 2831–2838, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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 MathSciNet
  5. Y. Yao, Y.-C. Liou, and R. Chen, “Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 12, pp. 3311–3317, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Zhou, “Viscosity approximation methods for pseudocontractive mappings in Banach spaces,” Nonlinear Analysis, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Y. Song and R. Chen, “Convergence theorems of iterative algorithms for continuous pseudocontractive mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 2, pp. 486–497, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. S. Liu, “Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 194, no. 1, pp. 114–125, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. 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 MathSciNet
  10. W. Takahashi, Nonlinear Functional Analysis. Fixed Point Theory and Its Applications, Yokohama Publishers, Yokohama, Japan, 2000. View at Zentralblatt MATH · View at MathSciNet