Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2010, Article ID 582475, 11 pages
http://dx.doi.org/10.1155/2010/582475
Research Article

Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan

Received 27 August 2010; Accepted 18 December 2010

Academic Editor: Mitsuharu Ôtani

Copyright © 2010 Yasunori Kimura. 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. W. A. Kirk, “Fixed point theorems in CAT(0) spaces and -trees,” Fixed Point Theory and Applications, vol. 2004, no. 4, pp. 309–316, 2004. View at Publisher · View at Google Scholar
  2. S. Dhompongsa, W. A. Kirk, and B. Sims, “Fixed points of uniformly Lipschitzian mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 65, no. 4, pp. 762–772, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. S. Dhompongsa, W. A. Kirk, and B. Panyanak, “Nonexpansive set-valued mappings in metric and Banach spaces,” Journal of Nonlinear and Convex Analysis, vol. 8, no. 1, pp. 35–45, 2007. View at Google Scholar · View at Zentralblatt MATH
  4. S. Saejung, “Halpern's iteration in CAT(0) spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 471781, 13 pages, 2010. View at Google Scholar · View at Zentralblatt MATH
  5. W. A. Kirk and B. Panyanak, “A concept of convergence in geodesic spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 12, pp. 3689–3696, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. T. C. Lim, “Remarks on some fixed point theorems,” Proceedings of the American Mathematical Society, vol. 60, pp. 179–182, 1976. View at Publisher · View at Google Scholar
  7. M. Tsukada, “Convergence of best approximations in a smooth Banach space,” Journal of Approximation Theory, vol. 40, pp. 301–309, 1984. View at Publisher · View at Google Scholar
  8. T. Ibaraki, Y. Kimura, and W. Takahashi, “Convergence theorems for generalized projections and maximal monotone operators in Banach spaces,” Abstract and Applied Analysis, no. 10, pp. 621–629, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. E. Resmerita, “On total convexity, Bregman projections and stability in Banach spaces,” Journal of Convex Analysis, vol. 11, no. 1, pp. 1–16, 2004. View at Google Scholar
  10. Y. Kimura, “A characterization of strong convergence for a sequence of resolvents of maximal monotone operators,” in Fixed Point Theory and Its Applications, pp. 149–159, Yokohama Publishers, Yokohama, Japan, 2006. View at Google Scholar · View at Zentralblatt MATH
  11. Y. Kimura, K. Nakajo, and W. Takahashi, “Strongly convergent iterative schemes for a sequence of nonlinear mappings,” Journal of Nonlinear and Convex Analysis, vol. 9, no. 3, pp. 407–416, 2008. View at Google Scholar · View at Zentralblatt MATH
  12. Y. Kimura and W. Takahashi, “On a hybrid method for a family of relatively nonexpansive mappings in a Banach space,” Journal of Mathematical Analysis and Applications, vol. 357, no. 2, pp. 356–363, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, vol. 319 of Grundlehren der. Mathematischen Wissenschaften, Springer, Berlin, Germany, 1999.
  14. 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
  15. U. Mosco, “Convergence of convex sets and of solutions of variational inequalities,” Advances in Mathematics, vol. 3, pp. 510–585, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, vol. 83 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1984.
  17. I. Shafrir, “Theorems of ergodic type for ρ-nonexpansive mappings in the Hilbert ball,” Annali di Matematica Pura ed Applicata, vol. 163, no. 1, pp. 313–327, 1993. View at Publisher · View at Google Scholar
  18. K. Aoyama and F. Kohsaka, “Existence of fixed points of firmly nonexpansive-like mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 512751, 15 pages, 2010. View at Google Scholar