Continuous solutions for a Volterra-Stieltjes quadratic integral equation
type: Item
instance of: scholarly article
title: Continuous solutions for a Volterra-Stieltjes quadratic integral equation
zbMATH Open document ID: 1098.45006
published in: Journal of the Egyptian Mathematical Society
publication date: 2006-03-29T00:00:00Z
review text: The author considers a quadratic Volterra-Stieltjes integral equation in the space \(BC(\mathbb{R}_+)\) consisting of real functions defined, continuous and bounded on \(\mathbb{R}_+= [0,+\infty)\) with supremum norm. It is shown that the mentioned integral equation has a solution in \(BC(\mathbb{R}_+)\) under some conditions. The main tool used in the proof is the technique of measures of noncompactness. The results of the paper seems to be not valid since the author uses a function being a kind of the modulus of continuity of a set as the measure of noncompactness in the space \(BC(\mathbb{R}_+)\). It is well-known that such a function is not a measure of noncompactness in \(BC(\mathbb{R}_+)\).
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5016031
zbMATH Keywords: quadratic Volterra-Stieltjes integral equation
zbMATH Keywords: measures of noncompactness
author: Wagdy Gomaa El-Sayed
reviewed by: Józef Banaś
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5016031