About this Journal Submit a Manuscript Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 843256, 3 pages
http://dx.doi.org/10.5402/2012/843256
Research Article

Brouwer's Fixed Point Theorem with Isolated Fixed Points and His Fan Theorem

Faculty of Economics, Doshisha University, Kamigyo-ku, Kyoto 602-8580, Japan

Received 2 October 2011; Accepted 10 November 2011

Academic Editor: T. Karakasidis

Copyright © 2012 Yasuhito Tanaka. 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. R. B. Kellogg, T. Y. Li, and J. Yorke, “A constructive proof of Brouwer fixed-point theorem and computational results,” SIAM Journal on Numerical Analysis, vol. 13, no. 4, pp. 473–483, 1976.
  2. D. Bridges and F. Richman, Varieties of Constructive Mathematics, Cambridge University Press, 1987.
  3. D. van Dalen, “Brouwer’s ε-fixed point from Sperner’s lemma,” Theoretical Computer Science, vol. 412, no. 28, pp. 3140–3144, 2011.
  4. W. Veldman, “Brouwer’s approximate fixed point theorem is equivalent to Brouwer’s fan theorem,” in Logicism, Intuitionism and Formalism, S. Lindström, E. Palmgren, K. Segerberg, and V. Stoltenberg-Hansen, Eds., Springer, 2009.
  5. J. Berger and H. Ishihara, “Brouwer's fan theorem and unique existence in constructive analysis,” Mathematical Logic Quarterly, vol. 51, no. 4, pp. 360–364, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Y. Tanaka, “Constructive proof of the existence of Nash equilibrium in a finite strategic game with sequentially locally nonconstant payoff functions,” ISRN Computational Mathematics, Article ID 459459, 8 pages, 2012. View at Publisher · View at Google Scholar
  7. D. Bridges and L. Vîţă, Techniques of Constructive Mathematics, Springer, 2006.
  8. J. Berger, D. Bridges, and P. Schuster, “The fan theorem and unique existence of maxima,” Journal of Symbolic Logic, vol. 71, no. 2, pp. 713–720, 2006. View at Publisher · View at Google Scholar