A Simplicial Approach for Discrete Fixed Point Theorems

  • Authors:

  • Xi Chen;Xiaotie Deng

  • Affiliations:

  • Tsinghua University, Department of Computer Science, Beijing, People’s Republic of China;City University of Hong Kong, Department of Computer Science, Kowloon, Hong Kong

  • Venue:
  • Algorithmica
  • Year:
  • 2009

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Abstract

We present a new discrete fixed point theorem based on a variation of the direction-preserving maps over simplicial structures. We show that the result is more general than the recent discrete fixed point theorem of Iimura et al. (J. Math. Econ. 41(8):1030–1036, [2005]) by deriving it 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.