A discrete fixed point theorem utilizing the direction preserving condition

Hidefumi Kawasaki, Shuhei Hashiyama

研究成果: Contribution to journalArticle査読

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.

本文言語英語
ページ(範囲)1535-1545
ページ数11
ジャーナルJournal of Nonlinear and Convex Analysis
18
8
出版ステータス出版済み - 1 1 2017

All Science Journal Classification (ASJC) codes

  • 分析
  • 幾何学とトポロジー
  • 制御と最適化
  • 応用数学

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