Gronwall-Bellman type integral inequalities for abstract Lebesgue integral
type: Item
instance of: scholarly article
title: Gronwall-Bellman type integral inequalities for abstract Lebesgue integral
zbMATH Open document ID: 0881.26006
DOI: 10.1016/S0895-7177(96)00184-7
published in: Mathematical and Computer Modelling
publication date: 1998-02-17T00:00:00Z
review text: In the present paper, the authors establish some new linear integral inequalities of the Gronwall-Bellman type for scalar functions of several variables involving abstract Lebesgue (especially Lebesgue-Stieltjes) integrals. Some delay and advance effects appear in the considered inequalities. The proofs given in the paper depend on some earlier work of the second author of the present paper [J. Math. Anal. Appl. 202, No. 1, 183-193 (1996; Zbl 0859.26008)]. An illustrating example is also given to convey the sharpness of the established results.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1042731
zbMATH Keywords: multidimensional integral inequality
zbMATH Keywords: integral equation
zbMATH Keywords: abstract Lebesgue integral
zbMATH Keywords: integral inequalities of the Gronwall-Bellman type
author: István Győri
author: László Horváth
MaRDI profile type: Publication
cites work: Q4003924
cites work: On an integral inequality in n independent variables
cites work: On some Gronwall-type integral inequalities in \(n\) independent variables
cites work: Systems of multidimensional volterra integral equations and inequalities
cites work: The Gronwall-Bellman inequality in several variables
cites work: Q4381171
cites work: On some new inequalities in n independent variables
cites work: On some new integrodifferential inequalities of the Gronwall and Wendroff type
cites work: Some Stieltjes integral inequalities
cites work: Stieltjes integral inequalities of Gronwall type and applications
cites work: A nonlinear Volterra-Stieltjes integral equation and a Gronwall inequality in one dimension
cites work: Q5653013
cites work: On systems of linear differentio-Stieltjes-integral equations
cites work: The Gronwall Inequality for Modified Stieltjes Integrals
cites work: Integral inequalities of Gronwall type for distributions
cites work: Gronwall-Bellman type integral inequalities in measure spaces
full work available at URL: s0895-7177(96)00184-7
OpenAlex ID: W1998951284
description: scientific article; zbMATH DE number 1042731