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Introduction to FK Spaces

In: Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations

Author

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  • Józef Banaś

    (Rzeszów University of Technology, Department of Mathematics)

  • Mohammad Mursaleen

    (Aligarh Muslim University, Department of Mathematics)

Abstract

In this chapter, we study the concepts of linear metric spaces, paranormed spaces, FK spaces and BK spaces which play an important role in our studies on sequence spaces. One of the main advantage of FK space theory is that it provides easy and short proofs of numerous classical results of summability theory and is the most powerful and widely used tool in the characterization of matrix mappings between sequence spaces. Moreover, it enables us to obtain the most important result on the continuity of matrix mappings between FK spaces. The results of the theory of FK and BK spaces are also applied to characterize the matrix classes.

Suggested Citation

  • Józef Banaś & Mohammad Mursaleen, 2014. "Introduction to FK Spaces," Springer Books, in: Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, edition 127, chapter 0, pages 1-32, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1886-9_1
    DOI: 10.1007/978-81-322-1886-9_1
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