Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 409898, 10 pages
http://dx.doi.org/10.1155/2011/409898
Review Article

Strong and Weak Convergence Theorems for an Infinite Family of Lipschitzian Pseudocontraction Mappings in Banach Spaces

1Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China
2Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received 16 December 2010; Accepted 9 February 2011

Academic Editor: Giuseppe Marino

Copyright © 2011 Shih-sen Chang 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. 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
  2. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
  3. S. Chang, Y. J. Cho, and H. Zhou, Iterative Methods for Nonlinear Operator Equations in Banach Spaces, Nova Science, Huntington, NY, USA, 2002.
  4. 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
  5. H.-K. Xu and R. G. Ori, “An implicit iteration process for nonexpansive mappings,” Numerical Functional Analysis and Optimization, vol. 22, no. 5-6, pp. 767–773, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. M. O. Osilike, “Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps,” Journal of Mathematical Analysis and Applications, vol. 294, no. 1, pp. 73–81, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. R. Chen, Y. Song, and H. Zhou, “Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings,” Journal of Mathematical Analysis and Applications, vol. 314, no. 2, pp. 701–709, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. Zhou, “Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 10, pp. 2977–2983, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. D. Boonchari and S. Saejung, “Construction of common fixed points of a countable family of λ-demicontractive mappings in arbitrary Banach spaces,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 173–178, 2010. View at Publisher · View at Google Scholar
  10. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990. View at Publisher · View at Google Scholar
  11. S.-S. Chang, “Some problems and results in the study of nonlinear analysis,” Nonlinear Analysis: Theory, Methods & Applications, vol. 30, no. 7, pp. 4197–4208, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. 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 & Applications, vol. 67, no. 8, pp. 2350–2360, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH