On a way of division of segments
type: Item
instance of: scholarly article
title: On a way of division of segments
zbMATH Open document ID: 0633.39001
DOI: 10.1007/BF01830671
published in: Aequationes Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137239
review text: The authors study the recurrent equation (1) \(a_{n,k}=a_{n+1,k}+a_{n+1,k+1}\), \(k=1,2,...,n\), \(n\in N\) with the initial condition \(a_{3,1}=u\), \(a_{3,2}=v\), \(a_{3,3}=w\). They prove that if u, v, w are positive numbers, then there exists a sequence \(a_{n,k}\) of positive numbers satisfying equation (1) if and only if \(v^ 2\leq uw\). The sequence is unique if and only if \(v^ 2=uw\). The authors show that the theorem above can be deduced from some results of \textit{M. Laczkovich}, obtained by using advanced tools [Non-negative measurable solutions of difference equations, J. London Math. Soc. 2, 139-147 (1986)] while the proof they present is completely elementary.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 4030116
zbMATH Keywords: recurrent equation
zbMATH Keywords: measurable solutions
zbMATH Keywords: difference equations
author: Karol Baron
author: Witold Jarczyk
reviewed by: Gian Luigi Forti
MaRDI profile type: Publication
cites work: Q3854084
cites work: Q4746949
cites work: Q3797635
cites work: Non-Negative Measurable Solutions of Difference Equations
OpenAlex ID: W1997446173
description: scientific article; zbMATH DE number 4030116