Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in \(\ell _{p} \) \((1<p< \infty)\)
type: Item
instance of: scholarly article
title: Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in \(\ell _{p} \) \((1<p< \infty)\)
zbMATH Open document ID: 1418.45008
author: Anupam Das
author: Bipan Hazarika
author: M. Mursaleen
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2019-03-26T00:00:00Z
review text: Since the pioneering work of G. Darbo and B. N. Sadovskij, measures of noncompactness and condensing operators have found a wealth of interesting applications, mainly to differential equations and integral equations in normed function spaces. An application-oriented survey of such applications may be found in [\textit{J. Appell}, Fixed Point Theory 6, No. 2, 157--229 (2005; Zbl 1102.47041)]. In this paper the authors apply the notion of so-called Meir-Keeler condensing operators [\textit{A. Aghajani} et al., Acta Math. Sci., Ser. B, Engl. Ed. 35, No. 3, 552--566 (2015; Zbl 1340.47103)] to solve an infinite system of integral equations of two variables in the sequence space $l_p$ for $1<p<\infty$. They also give a (rather artificial) example, but no application which illustrates the usefulness of their result.
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45F99
Mathematics Subject Classification ID: 47H08
zbMATH DE Number: 7042571
zbMATH Keywords: systems of integral equations
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: Hausdorff measure of noncompactness
zbMATH Keywords: condensing operators
zbMATH Keywords: fixed point
MaRDI profile type: Publication
full work available at URL: s13398-017-0452-1
OpenAlex ID: W2761368372
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DOI: 10.1007/S13398-017-0452-1
description: scientific article; zbMATH DE number 7042571