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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 863483, 20 pages
Review Article

Infinite System of Differential Equations in Some Spaces

1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 26 July 2012; Accepted 1 October 2012

Academic Editor: Beata Rzepka

Copyright © 2012 M. Mursaleen and Abdullah Alotaibi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 .