Nonlinear Hammerstein equations and functions of bounded Riesz-Medvedev variation
type: Item
instance of: scholarly article
title: Nonlinear Hammerstein equations and functions of bounded Riesz-Medvedev variation
zbMATH Open document ID: 1366.45004
DOI: 10.12775/TMNA.2016.008
author: Jürgen Appell
author: Tomás Domínguez Benavides
published in: Topological Methods in Nonlinear Analysis
publication date: 2017-04-04T00:00:00Z
review text: The authors consider the solvability of the Hammerstein integral equation \[ f(s)=\int_a^bk(s,t)h(t,f(t))\,dt+b(s). \] The main novelty of the paper seems to be the allowance of very weak regularity assumptions on the constituent functions in the integral equation and, in particular, the search for solutions of the equation within spaces of generalized bounded variation. While it is unfortunate that no concrete examples are provided to illustrate the abstract theory, the paper is relatively clearly written, and it should be of interest to researchers whose interests intersect existence theory for integral equations.
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 26A45
Mathematics Subject Classification ID: 26A46
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 6700541
zbMATH Keywords: bounded variation
zbMATH Keywords: nonlinear integral equation
zbMATH Keywords: fixed point theorem
zbMATH Keywords: Orlicz space
zbMATH Keywords: Hammerstein integral equation
reviewed by: Christopher Goodrich
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6700541