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Journal of Applied Mathematics
Volume 2014, Article ID 981494, 6 pages
http://dx.doi.org/10.1155/2014/981494
Research Article

Strong Convergence of a Modified Ishikawa Iterative Sequence for Asymptotically Quasi-Pseudo-Contractive-Type Mappings

Department of Mathematics, Xingzhi College, Zhejiang Normal University, Zhejiang 321004, China

Received 20 January 2014; Accepted 19 February 2014; Published 26 March 2014

Academic Editor: Li Wei

Copyright © 2014 Liuhong Li and Yuanheng Wang. 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, “Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 129, no. 3, pp. 845–853, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Schu, “Iterative construction of fixed points of asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 158, no. 2, pp. 407–413, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. L. Zeng, “Modified Ishikawa iteration process with errors in Banach,” Acta Mathematica Sinica, vol. 47, no. 2, pp. 219–228, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Zeng, “On the strong convergence of iterative method for non-Lipschitzian asymptotically pseudocontractive mappings,” Acta Mathematicae Applicatae Sinica, vol. 27, no. 3, pp. 230–239, 2004. View at Google Scholar · View at Zentralblatt MATH
  6. Y. Yao, R. Chen, G. Marino, and Y.-C. Liou, “Applications of fixed point and approximate algorithms,” Journal of Applied Mathematics, vol. 2012, Article ID 175459, 2 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. L. Wei, Y.-F. Su, and H.-Y. Zhou, “New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators,” Applied Mathematics, vol. 25, no. 2, pp. 199–208, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. D. Zhang, X. Qin, and F. Gu, “Approximation of common fixed points of nonexpansive semigroups in Hilbert spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 417234, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. L.-C. Ceng and C.-F. Wen, “Composite iterative algorithms for variational inequality and fixed point problems in real smooth and uniformly convex Banach spaces,” Journal of Applied Mathematics, vol. 2013, Article ID 761864, 21 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L.-C. Ceng, H.-K. Xu, and C.-F. Wen, “Relaxed viscosity approximation methods with regularization for constrained minimization problems,” Journal of Applied Mathematics, vol. 2013, Article ID 531859, 19 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. L.-C. Ceng and C.-F. Wen, “Hybrid method with perturbation for Lipschitzian pseudo-contractions,” Journal of Applied Mathematics, vol. 2012, Article ID 250538, 20 pages, 2012. View at Publisher · View at Google Scholar
  12. R. E. Bruck, T. Kuczumow, and S. Reich, “Convergence of Iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property,” Colloquium Mathematicum, vol. 65, no. 2, pp. 169–179, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. L. Zeng, “On the Iterative construction of fixed points of asymptotically pseudo-contractive type mappings,” Journal of Systems Science and Mathematical Sciences, vol. 24, pp. 261–270, 2004. View at Google Scholar
  14. Y. Wang, “Strong convergence theorems for asymptotically weak G-pseudo-ψ-contractive non-self-mappings with the generalized projection in Banach spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 651304, 11 pages, 2012. View at Publisher · View at Google Scholar
  15. C. Moore and B. V. C. Nnoli, “Iterative solution of nonlinear equations involving set-valued uniformly accretive operators,” Computers and Mathematics with Applications, vol. 42, no. 1-2, pp. 131–140, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus