A discrete fixed point theorem utilizing the direction preserving condition

Hidefumi Kawasaki, Shuhei Hashiyama

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)1535-1545
Number of pages11
JournalJournal of Nonlinear and Convex Analysis
Volume18
Issue number8
Publication statusPublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

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

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