A constructive proof of Ky Fan’s coincidence theorem

  • Authors:

  • A. J. J. Talman;Z. Yang

  • Affiliations:

  • Tilburg University, CentER, Department of Econometrics and Operations Research, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands;Yokohama National University, Faculty of Business Administration, 240-8501, Yokohama, Japan

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2009

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Abstract

We present a constructive proof for the well-known Ky Fan’s coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point.