Three fixed points of ray avoiding mappings on a finite-dimensional space
type: Item
instance of: scholarly article
title: Three fixed points of ray avoiding mappings on a finite-dimensional space
zbMATH Open document ID: 0966.47036
DOI: 10.1016/S0895-7177(00)00155-2
published in: Mathematical and Computer Modelling
publication date: 2001-08-08T00:00:00Z
review text: If the reviewer understands the paper correctly, the author deals with the following situation: Let \(D\subset\mathbb{R}^n\) be a nonempty, compact convex set and call \(r:\mathbb{R}^n\to D\) the metric projection with respect to the Euclidean norm. Let \(h,k>0\). A continuous map \(A:D\to\mathbb{R}^n\) is said to be ray avoiding if the following conditions are satisfied: 1) For sufficiently large \(c>0\), we have that \(\tau Arx\not=x\) whenever \(0<\tau\leq 1-k/c\) and \(d(x,rx)=h/c\) where \(d\) is the metric associated to the max-norm. 2) Whenever \(V\) is relatively open in \(D\) and \(x\in V\) we have that \((1-k/c)x\in r^{-1}(V)\cap\{x|\;d(x,rx)<h/c\}\). Starting from the Brouwer degree the author defines a fixed point index for ray avoiding maps. He then uses this index to formulate conditions for a ray avoiding map \(A\) that imply the existence of three fixed points of \(A\).
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1545778
zbMATH Keywords: fixed point
zbMATH Keywords: Brouwer degree
zbMATH Keywords: metric projection
zbMATH Keywords: ray avoiding maps
zbMATH Keywords: index
author: Richard I. Avery
reviewed by: Christian Fenske
MaRDI profile type: Publication
cites work: Multiple positive fixed points of weakly inward mappings
cites work: Q3854213
cites work: Q5185568
cites work: Q4716258
cites work: Multiple positive solutions to a third-order discrete focal boundary value problem
cites work: Q4526471
cites work: Q3994493
cites work: Q4000373
cites work: Q3706042
full work available at URL: s0895-7177(00)00155-2
OpenAlex ID: W1996843533
description: scientific article; zbMATH DE number 1545778