Infinite System of Differential Equations in Some Spaces

Infinite System of Differential Equations in Some Spaces

The first measure of noncompactness was defined by Kuratowski in 1930 and later the Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al. These measures of noncompactness have various applications in several areas of analysis, for example, in operator theory, fixed point t...

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Main Authors: M. Mursaleen, Abdullah Alotaibi
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/863483
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spelling doaj-11bb7db19e754ec9a2f82083a86da6222020-11-24T22:00:50ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/863483863483Infinite System of Differential Equations in Some SpacesM. Mursaleen0Abdullah Alotaibi1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe first measure of noncompactness was defined by Kuratowski in 1930 and later the Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al. These measures of noncompactness have various applications in several areas of analysis, for example, in operator theory, fixed point theory, and in differential and integral equations. In particular, the Hausdorff measure of noncompactness has been extensively used in the characterizations of compact operators between the infinite-dimensional Banach spaces. In this paper, we present a brief survey on the applications of measures of noncompactness to the theory of infinite system of differential equations in some spaces and .http://dx.doi.org/10.1155/2012/863483
collection DOAJ
language English
format Article
sources DOAJ
author M. Mursaleen
Abdullah Alotaibi
spellingShingle M. Mursaleen
Abdullah Alotaibi
Infinite System of Differential Equations in Some Spaces
Abstract and Applied Analysis
author_facet M. Mursaleen
Abdullah Alotaibi
author_sort M. Mursaleen
title Infinite System of Differential Equations in Some Spaces
title_short Infinite System of Differential Equations in Some Spaces
title_full Infinite System of Differential Equations in Some Spaces
title_fullStr Infinite System of Differential Equations in Some Spaces
title_full_unstemmed Infinite System of Differential Equations in Some Spaces
title_sort infinite system of differential equations in some spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description The first measure of noncompactness was defined by Kuratowski in 1930 and later the Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al. These measures of noncompactness have various applications in several areas of analysis, for example, in operator theory, fixed point theory, and in differential and integral equations. In particular, the Hausdorff measure of noncompactness has been extensively used in the characterizations of compact operators between the infinite-dimensional Banach spaces. In this paper, we present a brief survey on the applications of measures of noncompactness to the theory of infinite system of differential equations in some spaces and .
url http://dx.doi.org/10.1155/2012/863483
work_keys_str_mv AT mmursaleen infinitesystemofdifferentialequationsinsomespaces
AT abdullahalotaibi infinitesystemofdifferentialequationsinsomespaces
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