On existence of extremal solutions of nonlinear functional integral equations in Banach algebras
type: Item
instance of: scholarly article
title: On existence of extremal solutions of nonlinear functional integral equations in Banach algebras
zbMATH Open document ID: 1088.47051
DOI: 10.1155/S1048953304308038
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2005-03-21T00:00:00Z
full work available at URL: https://eudml.org/doc/52386
review text: Let \(K\) be a normal and positive cone of a real Banach algebra \(X\) and let \(u\), \(v\in X\) be such that \(u\leq v\). The author proves the existence of a least solution and a greatest one of the operator equation \[ AxBx+Cx=x \] in \([u,v]\), where \(A\), \(B:[u,v]\to K\) and \(C:[u,v]\to X\) satisfy some suitable conditions. Applications to a functional integral equation of mixed type are also given.
reviewed by: Mirosława Zima
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H07
zbMATH DE Number: 2148080
zbMATH Keywords: Banach algebra
zbMATH Keywords: cone
zbMATH Keywords: operator equation
zbMATH Keywords: functional integral equation
zbMATH Keywords: extremal solution
author: Bapurao C. Dhage
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2148080