About this Journal Submit a Manuscript Table of Contents 
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 730619, 7 pages
doi:10.1155/2012/730619
Review Article

On the Weak Relatively Nonexpansive Multivalued Mappings in Banach Spaces

Yongfu Su

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 12 July 2012; Accepted 7 August 2012

Academic Editor: Xiaolong Qin

Copyright © 2012 Yongfu Su. 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. Y. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, A. G. Kartosatos, Ed., vol. 178 of Lecture Notes in Pure and Applied Mathematics, pp. 15–50, Marcel Dekker, New York, NY, USA, 1996. View at Zentralblatt MATH
  2. S. Homaeipour and A. Razani, “Weak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2011, article 73, 2011.
  3. S. Matsushita and W. Takahashi, “A strong convergence theorem for relatively nonexpansive mappings in a Banach space,” Journal of Approximation Theory, vol. 134, no. 2, pp. 257–266, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. W. Takahashi and K. Zembayashi, “Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 1, pp. 45–57, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. X. Qin and Y. Su, “Strong convergence theorems for relatively nonexpansive mappings in a Banach space,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 6, pp. 1958–1965, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Y. F. Su, J. Y. Gao, and H. Y. Zhou, “Monotone CQ algorithm of fixed points for weak relatively nonexpansive mappings and applications,” Journal of Mathematical Research and Exposition, vol. 28, no. 4, pp. 957–967, 2008. View at Zentralblatt MATH
  7. H. Zegeye and N. Shahzad, “Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 7, pp. 2707–2716, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. Su, D. Wang, and M. Shang, “Strong convergence of monotone hybrid algorithm for hemi-relatively nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2008, Article ID 284613, 8 pages, 2008. View at Zentralblatt MATH
  9. Y. Su, Z. Wang, and H. Xu, “Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 11, pp. 5616–5628, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH