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 |
|---|---|
| ページ（範囲） | 1535-1545 |
| ページ数 | 11 |
| ジャーナル | Journal of Nonlinear and Convex Analysis |
| 巻 | 18 |
| 発行部数 | 8 |
| 出版物ステータス | 出版済み - 2017 |
| 外部発表 | Yes |
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All Science Journal Classification (ASJC) codes
- Analysis
- Geometry and Topology
- Control and Optimization
- Applied Mathematics
これを引用
A discrete fixed point theorem utilizing the direction preserving condition. / Kawasaki, Hidefumi; Hashiyama, Shuhei.
：: Journal of Nonlinear and Convex Analysis, 巻 18, 番号 8, 2017, p. 1535-1545.研究成果: ジャーナルへの寄稿 › 記事
}
TY - JOUR
T1 - A discrete fixed point theorem utilizing the direction preserving condition
AU - Kawasaki, Hidefumi
AU - Hashiyama, Shuhei
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=85030759333&partnerID=8YFLogxK
M3 - Article
VL - 18
SP - 1535
EP - 1545
JO - Journal of Nonlinear and Convex Analysis
JF - Journal of Nonlinear and Convex Analysis
SN - 1345-4773
IS - 8
ER -