Generalizations of Darbo's fixed point theorem for new condensing operators with application to a functional integral equation
type: Item
instance of: scholarly article
title: Generalizations of Darbo's fixed point theorem for new condensing operators with application to a functional integral equation
zbMATH Open document ID: 1477.47040
author: Habib ur Rehman
author: Dhananjay Gopal
author: Poom Kumam
published in: Demonstratio Mathematica
publication date: 2019-06-27T00:00:00Z
review text: The authors define a new class of nonlinear operators which are condensing in a weak sense, depending on certain auxiliary functions \(\alpha\) and \(\beta\). They obtain a corresponding fixed point theorem which contains Darbo's fixed point principle for a special choice of \(\alpha\) and \(\beta\), and apply this to the functional-integral equation \[x(t)= A(t)+ h(t,x(\xi(t)))+ f(t, x(\xi(t)), \varphi(Gx(t)))\qquad (t\ge 0),\] where \(G\) is the functional-integral operator of Uryson type \[Gx(t):= \int^{\beta(t)}_0 g(t,s,x(\eta(s)))\,ds.\] The paper contains some inexact points; for instance, Example 1.7 does not make sense.
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 7074049
zbMATH Keywords: Darbo fixed point theorem
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: fixed point
zbMATH Keywords: coupled fixed point
zbMATH Keywords: functional integral equation
reviewed by: Jürgen Appell
MaRDI profile type: Publication
full work available at URL: dema-2019-0012
OpenAlex ID: W2923928938
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Wikidata QID: Q128169124
DOI: 10.1515/DEMA-2019-0012
description: scientific article; zbMATH DE number 7074049