# A discrete fixed point theorem utilizing the direction preserving condition

Hidefumi Kawasaki, Shuhei Hashiyama

### 抄録

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 ℝ2 and the Preudenthal decomposition in ℝn. Next we characterize the direction preserving condition for an arbitrary consistent simplicial decomposition in ℝn, which implies a sufficient condition for the strategic game to have a pure-strategy equilibrium.

元の言語 英語 1535-1545 11 Journal of Nonlinear and Convex Analysis 18 8 出版済み - 2017 Yes

### Fingerprint

Fixed point theorem
Decomposition
Decompose
Brouwer Fixed Point Theorem
Arbitrary
Convex Hull
Rectangle
Fixed point
Game
Imply
Integer
Sufficient Conditions

### All Science Journal Classification (ASJC) codes

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

### これを引用

：: Journal of Nonlinear and Convex Analysis, 巻 18, 番号 8, 2017, p. 1535-1545.

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