Abstract
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.
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Chen, X., Deng, X. (2006). A Simplicial Approach for Discrete Fixed Point Theorems. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_3
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DOI: https://doi.org/10.1007/11809678_3
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