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A Simplicial Approach for Discrete Fixed Point Theorems

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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.

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Authors and Affiliations

  1. Department of Computer Science, Tsinghua University, Beijing, People’s Republic of China

    Xi Chen

  2. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

    Xiaotie Deng

Authors
  1. Xi Chen
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  2. Xiaotie Deng
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Correspondence to Xi Chen.

Additional information

X. Chen work was supported in part by the National Natural Science Foundation of China Grant (60553001), and the National Basic Research Program of China Grant (2007CB807900, 2007CB807901).

X. Deng work supported by an SRG grant (No. 7001975) of City University of Hong Kong and an NNSFC grant (No. 60496327).

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Chen, X., Deng, X. A Simplicial Approach for Discrete Fixed Point Theorems. Algorithmica 53, 250–262 (2009). https://doi.org/10.1007/s00453-008-9183-1

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  • DOI: https://doi.org/10.1007/s00453-008-9183-1

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