## Abstract

This paper aims to characterize the direction preserving condition that guarantees the existence of a fixed point of discrete mappings defined on an integer rectangle X into itself. We deal with a discrete fixed point theorem based on Brouwer's fixed point theorem, which depends on the simplicial decomposition of the convex hull of X. We first review an arbitrary simplicial decomposition in ℝ^{2} and the Preudenthal decomposition in ℝ^{n}. Next we characterize the direction preserving condition for an arbitrary consistent simplicial decomposition in ℝ^{n}, which implies a sufficient condition for the strategic game to have a pure-strategy equilibrium.

Original language | English |
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Pages (from-to) | 1535-1545 |

Number of pages | 11 |

Journal | Journal of Nonlinear and Convex Analysis |

Volume | 18 |

Issue number | 8 |

Publication status | Published - 2017 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Geometry and Topology
- Control and Optimization
- Applied Mathematics