A constructive proof of Ky Fan’s coincidence theorem |
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Authors: | A. J. J. Talman Z. Yang |
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Affiliation: | (1) CentER, Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands;(2) Faculty of Business Administration, Yokohama National University, Yokohama 240-8501, Japan |
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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. This research was carried out while the second author was visiting the CentER for Economic Research, Tilburg University. He would like to thank both CentER and the Netherlands Organization for Scientific Research (NWO) for their financial support. |
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Keywords: | Fan’ s coincidence theorem Fixed point Simplicial algorithm Upper semi-continuity |
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