Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 275607, 7 pages
http://dx.doi.org/10.1155/2014/275607
Research Article

Weak and Strong Convergence Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 6 February 2014; Accepted 14 May 2014; Published 27 May 2014

Academic Editor: Nan-Jing Huang

Copyright © 2014 Lei Deng and Juan Xiao. 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. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. E. Rhoades and S. M. Soltuz, “The equivalence between Mann-Ishikawa iterations and multistep iteration,” Nonlinear Analysis. Theory, Methods & Applications, vol. 58, no. 1-2, pp. 219–228, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. C. E. Chidume and B. Ali, “Weak and strong convergence theorems for finite families of asymptotically nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 377–387, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. S. Chang, H. W. Joseph Lee, and C. K. Chan, “On Reich's strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 66, no. 11, pp. 2364–2374, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. Schu, “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings,” Bulletin of the Australian Mathematical Society, vol. 43, no. 1, pp. 153–159, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Suantai, “Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 506–517, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. O. Osilike and S. C. Aniagbosor, “Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 32, no. 10, pp. 1181–1191, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. Zhou and S.-S. Chang, “Convergence of implicit iteration process for a finite family of asymptotically nonexpansive mappings in Banach spaces,” Numerical Functional Analysis and Optimization, vol. 23, no. 7-8, pp. 911–921, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. E. Chidume, E. U. Ofoedu, and H. Zegeye, “Strong and weak convergence theorems for asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 280, no. 2, pp. 364–374, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. E. Chidume and N. Shahzad, “Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 62, no. 6, pp. 1149–1156, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet