A connection between fixed-point theorems and tiling problems
type: Item
instance of: scholarly article
title: A connection between fixed-point theorems and tiling problems
zbMATH Open document ID: 0983.54047
author: J. Jachymski
author: James D. Stein
author: Bernd Schröder
published in: Journal of Combinatorial Theory. Series A
publication date: 2002-04-23T00:00:00Z
review text: This paper mainly studies generalizations of the Banach contraction principle which states that any contraction on a complete metric space has a unique fixed point. A method for attacking such problems by considering a related problem on tiling the integers is developed. This technique simultaneously automates many of the unwieldy arguments, and makes for more visual proofs. The authors hope that presenting this combinatorial approach will serve a dual purpose: to stimulate the investigation of other analytical problems through combinatorics, and also to generate an interesting class of combinatorial problems.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 1340115
zbMATH Keywords: Banach contraction principle
reviewed by: Bai Kishan Dass
MaRDI profile type: Publication
full work available at URL: jcta.1998.2960
OpenAlex ID: W1996138726
cites work: A Remark on a Fixed-Point Theorem for Iterated Mappings
cites work: Q4254422
cites work: Q3210542
cites work: Q3995847
cites work: Uniformly Contractive Fixed Points in Compact Metric Spaces
cites work: A Comparison of Various Definitions of Contractive Mappings
DOI: 10.1006/JCTA.1998.2960
description: scientific article; zbMATH DE number 1340115