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Infinite System of Differential Equations in Some BK Spaces

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  • M. Mursaleen
  • Abdullah Alotaibi

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 BK spaces c0, c, ℓp(1 ≤ p ≤ ∞) and n(ϕ).

Suggested Citation

  • M. Mursaleen & Abdullah Alotaibi, 2012. "Infinite System of Differential Equations in Some BK Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:863483
    DOI: 10.1155/2012/863483
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    References listed on IDEAS

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    1. M. Mursaleen & A. Latif, 2012. "Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, March.
    2. M. Mursaleen & A. Latif, 2012. "Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Bruno De Malafosse & Eberhard Malkowsky & Vladimir Rakocevic, 2006. "Measure of noncompactness of operators and matrices on the spaces c and c 0," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-5, April.
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    Cited by:

    1. Józef Banaś & Kishin Sadarangani, 2013. "Compactness Conditions in the Study of Functional, Differential, and Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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