Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 327434, 17 pages
http://dx.doi.org/10.1155/2012/327434
Research Article

Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 26 October 2011; Accepted 8 December 2011

Academic Editor: Rudong Chen

Copyright © 2012 P. Pasom and B. Panyanak. 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 and H.-K. Xu, “Asymptotic pointwise contractions,” Nonlinear Analysis, vol. 69, no. 12, pp. 4706–4712, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. N. Hussain and M. A. Khamsi, “On asymptotic pointwise contractions in metric spaces,” Nonlinear Analysis, vol. 71, no. 10, pp. 4423–4429, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. W. M. Kozlowski, “Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 377, no. 1, pp. 43–52, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. R. Khan, A.-A. Domlo, and H. Fukhar-ud-din, “Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 1–11, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, vol. 319 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 1999.
  6. W. A. Kirk, “Fixed point theorems in CAT(0) spaces and -trees,” Fixed Point Theory and Applications, no. 4, pp. 309–316, 2004. View at Publisher · View at Google Scholar
  7. K. S. Brown, Buildings, Springer, New York, NY, USA, 1989.
  8. 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.
  9. W. A. Kirk, “Geodesic geometry and fixed point theory,” in Seminar of Mathematical Analysis, vol. 64 of Colecc. Abierta, pp. 195–225, Universidad de Sevilla Secr. Publ., Seville, Spain, 2003. View at Google Scholar · View at Zentralblatt MATH
  10. W. A. Kirk, “Geodesic geometry and fixed point theory. II,” in International Conference on Fixed Point Theory and Applications, pp. 113–142, Yokohama Publishers, Yokohama, Japan, 2004. View at Google Scholar · View at Zentralblatt MATH
  11. S. Dhompongsa, A. Kaewkhao, and B. Panyanak, “Lim's theorems for multivalued mappings in CAT(0) spaces,” Journal of Mathematical Analysis and Applications, vol. 312, no. 2, pp. 478–487, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. P. Chaoha and A. Phon-on, “A note on fixed point sets in CAT(0) spaces,” Journal of Mathematical Analysis and Applications, vol. 320, no. 2, pp. 983–987, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. L. Leustean, “A quadratic rate of asymptotic regularity for CAT(0)-spaces,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 386–399, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. S. Dhompongsa and B. Panyanak, “On Δ-convergence theorems in CAT(0) spaces,” Computers & Mathematics with Applications, vol. 56, no. 10, pp. 2572–2579, 2008. View at Publisher · View at Google Scholar
  15. N. Shahzad and J. Markin, “Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces,” Journal of Mathematical Analysis and Applications, vol. 337, no. 2, pp. 1457–1464, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. N. Shahzad, “Fixed point results for multimaps in CAT(0) spaces,” Topology and Its Applications, vol. 156, no. 5, pp. 997–1001, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. R. Espínola and A. Fernández-León, “CAT(k)-spaces, weak convergence and fixed points,” Journal of Mathematical Analysis and Applications, vol. 353, no. 1, pp. 410–427, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. A. Razani and H. Salahifard, “Invariant approximation for CAT(0) spaces,” Nonlinear Analysis, vol. 72, no. 5, pp. 2421–2425, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. S. Saejung, “Halpern's iteration in CAT(0) spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 471781, 13 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. A. R. Khan, M. A. Khamsi, and H. Fukhar-ud-din, “Strong convergence of a general iteration scheme in CAT(0) spaces,” Nonlinear Analysis, vol. 74, no. 3, pp. 783–791, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. S. H. Khan and M. Abbas, “Strong and Δ-convergence of some iterative schemes in CAT(0) spaces,” Computers & Mathematics with Applications, vol. 61, no. 1, pp. 109–116, 2011. View at Publisher · View at Google Scholar
  22. A. Abkar and M. Eslamian, “Common fixed point results in CAT(0) spaces,” Nonlinear Analysis, vol. 74, no. 5, pp. 1835–1840, 2011. View at Publisher · View at Google Scholar
  23. M. Bestvina, “-trees in topology, geometry, and group theory,” in Handbook of Geometric Topology, pp. 55–91, North-Holland, Amsterdam, The Netherlands, 2002. View at Google Scholar · View at Zentralblatt MATH
  24. C. Semple and M. Steel, Phylogenetics, vol. 24 of Oxford Lecture Series in Mathematics and Its Applications, Oxford University Press, Oxford, UK, 2003.
  25. R. Espínola and W. A. Kirk, “Fixed point theorems in -trees with applications to graph theory,” Topology and Its Applications, vol. 153, no. 7, pp. 1046–1055, 2006. View at Publisher · View at Google Scholar
  26. W. A. Kirk, “Some recent results in metric fixed point theory,” Journal of Fixed Point Theory and Applications, vol. 2, no. 2, pp. 195–207, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. S. Dhompongsa, W. A. Kirk, and B. Sims, “Fixed points of uniformly Lipschitzian mappings,” Nonlinear Analysis, vol. 65, no. 4, pp. 762–772, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. W. A. Kirk and B. Panyanak, “A concept of convergence in geodesic spaces,” Nonlinear Analysis, vol. 68, no. 12, pp. 3689–3696, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. T. C. Lim, “Remarks on some fixed point theorems,” Proceedings of the American Mathematical Society, vol. 60, pp. 179–182, 1976. View at Google Scholar
  30. 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
  31. W. A. Kirk, “A fixed point theorem for mappings which do not increase distances,” The American Mathematical Monthly, vol. 72, pp. 1004–1006, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  32. 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
  33. R. Espínola and N. Hussain, “Common fixed points for multimaps in metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 204981, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  34. P. Pasom and B. Panyanak, “Common fixed points for asymptotic pointwise nonexpansive mappings,” Fixed Point Theory. to appear.
  35. R. E. Bruck, Jr., “A common fixed point theorem for a commuting family of nonexpansive mappings,” Pacific Journal of Mathematics, vol. 53, pp. 59–71, 1974. View at Google Scholar · View at Zentralblatt MATH
  36. Z.-H. Sun, “Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 286, no. 1, pp. 351–358, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  37. M. A. Khamsi and A. R. Khan, “Inequalities in metric spaces with applications,” Nonlinear Analysis, vol. 74, no. 12, pp. 4036–4045, 2011. View at Publisher · View at Google Scholar
  38. B. Nanjaras and B. Panyanak, “Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 268780, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  39. R. 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