## Abstract and Applied Analysis

### Infinite System of Differential Equations in Some $\mathrm{BK}$ Spaces

#### Abstract

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 $\mathrm{BK}$ spaces ${c}_{0},c,{\ell }_{p}(1\le p\le \infty )$ and $n(\varphi )$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 863483, 20 pages.

Dates
First available in Project Euclid: 7 May 2014

https://projecteuclid.org/euclid.aaa/1399486657

Digital Object Identifier
doi:10.1155/2012/863483

Mathematical Reviews number (MathSciNet)
MR2999878

Zentralblatt MATH identifier
1258.28006

#### Citation

Mursaleen, M.; Alotaibi, Abdullah. Infinite System of Differential Equations in Some $\mathrm{BK}$ Spaces. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 863483, 20 pages. doi:10.1155/2012/863483. https://projecteuclid.org/euclid.aaa/1399486657

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