A Simplicial Approach for Discrete Fixed Point Theorems

  • Xi Chen
  • Xiaotie Deng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


We present a new discrete fixed point theorem based on a novel definition of direction-preserving maps over simplicial structures. We show that the result is more general and simpler than the two recent discrete fixed point theorems by deriving both of them from ours. The simplicial approach applied in the development of the new theorem reveals a clear structural comparison with the classical approach for the continuous case.


Nash Equilibrium Point Theorem Simple Corollary Simplicial Decomposition Simplicial Direction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xi Chen
    • 1
  • Xiaotie Deng
    • 2
  1. 1.Department of Computer ScienceTsinghua University 
  2. 2.Department of Computer ScienceCity University of Hong Kong 

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