A Simplicial Approach for Discrete Fixed Point Theorems
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.
fixed point theorem direction-preserving map simplicial structure sperner's lemma