The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally,...

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Main Authors: Józef Banaś, Szymon Dudek
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/537897
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spelling doaj-898ed98d240b4ab78c1ff7f9986b36112020-11-25T00:32:51ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/537897537897The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral EquationsJózef Banaś0Szymon Dudek1Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 8, 35-959 Rzeszów, PolandDepartment of Mathematics and Natural Sciences, State Higher School of Technology and Economics in Jarosław, Czarnieckiego 16, 37-500 Jarosław, PolandWe study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.http://dx.doi.org/10.1155/2013/537897
collection DOAJ
language English
format Article
sources DOAJ
author Józef Banaś
Szymon Dudek
spellingShingle Józef Banaś
Szymon Dudek
The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations
Abstract and Applied Analysis
author_facet Józef Banaś
Szymon Dudek
author_sort Józef Banaś
title The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations
title_short The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations
title_full The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations
title_fullStr The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations
title_full_unstemmed The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations
title_sort technique of measures of noncompactness in banach algebras and its applications to integral equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.
url http://dx.doi.org/10.1155/2013/537897
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