On Volterra-Fredholm integral equations
type: Item
instance of: scholarly article
title: On Volterra-Fredholm integral equations
zbMATH Open document ID: 0789.45005
DOI: 10.1007/BF01875881
author: A. S. S. Zaghrout
published in: Periodica Mathematica Hungarica
publication date: 1994-03-01T00:00:00Z
review text: The Ważewski method associated with the convergence of successive approximations is used in order to obtain existence and uniqueness results for the functional-integral equation of Volterra-Fredholm type of the form \[ \begin{multlined} x(t)=F \Biggl( t,x(t), \int_ 0^ t f_ 1(t,s,x(s))ds,\dots, \int_ 0^ t f_ n(t,s,x(s))ds,\\ \int_ 0^ T g_ 1(t,s,x(s))ds,\dots, \int_ 0^ T g_ n(t,s,x(s))ds \Biggr),\quad t\in[0,T].\end{multlined} \] It is assumed that the values of the functions involved belong to a Banach space. The reader is advised to be careful while reading this paper as there are some mistakes and misprints in the text.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 508825
zbMATH Keywords: Ważewski method
zbMATH Keywords: convergence
zbMATH Keywords: successive approximations
zbMATH Keywords: functional- integral equation of Volterra-Fredholm type
zbMATH Keywords: Banach space
reviewed by: Józef Banaś
MaRDI profile type: Publication
cites work: Q4118382
cites work: Q5524711
cites work: Existence and Stability of a Class of Nonlinear Volterra Integral Equations
cites work: Q5631657
cites work: Q3894443
full work available at URL: https://doi.org/10.1007/bf01875881
OpenAlex ID: W2135418952
description: scientific article; zbMATH DE number 508825