Systems of multidimensional discrete inequalities
type: Item
instance of: scholarly article
title: Systems of multidimensional discrete inequalities
zbMATH Open document ID: 0676.26009
DOI: 10.1016/0022-247X(89)90105-4
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: The paper is devoted to the study of the Gronwall's type discrete inequality \[ u(x)\leq a(x)+\sum^{x-1}_{s=0}K(x,s)u(s), \] where u and a are m-vector functions, K is a \(m\times m\) nonnegative matrix, \(x\in N^ n.\) In the main part of the paper the kernel K is separable, that is \(K(x,s)=G(x)H(s),\) where G,H are \(m\times m\) matrices. The best possible estimation is presented by a discrete analogue of \(m\times m\) matrix Riemann's function. Using the method of splitting or the method of maxima the author gives explicit bounds for the function u(x) or \(\max_{1\leq j\leq m}u_ j(x),\) respectively.
reviewed by: Jerzy Ryszard Popenda
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 4107137
zbMATH Keywords: vector-valued Riemann's function
zbMATH Keywords: Gronwall's type discrete inequality
author: Ravi P. Agarwal
MaRDI profile type: Publication
cites work: Q4106599
cites work: On an integral inequality in n independent variables
cites work: Q3710732
cites work: Q3781297
cites work: Q3343083
cites work: Q3695522
cites work: Linear Generalizations of Gronwall's Inequality
cites work: Shorter Notes: A Note on an Inequality Due to Greene
cites work: Q3322341
cites work: ON THE DISCRETE ANALOGY OF GRONWALL - WENDROFF INEQUALITY Jerzy Popenda
cites work: Q3346514
cites work: On some new inequalities in n independent variables
cites work: Shorter Notes: A Short Proof of a Greene Theorem
cites work: Discrete inequalities of the Gronwall-Bellman type in n independent variables
cites work: Discrete inequalities of the Gronwall-Bellman type in n independent variables. II
cites work: A note on Bellman-Gronwall's inequality
description: scientific article; zbMATH DE number 4107137