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Some Non-classical Sequence Spaces

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

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Abstract

In this chapter, we study the sequence spaces of Maddox and Nakano type, i.e. the spaces \(\ell (p),c_{0}(p),c(p),\ell _{\infty }(p)\) and \(w(p)\). We determine their duals, matrix transformations and their applications to study some new sequence spaces. We also study the sequence spaces \(m(\phi )\) and \(n(\phi )\) introduced by Sargent which are related to the spaces \(\ell _{p}\).

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Authors and Affiliations

  1. Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959, Rzeszow, Poland

    Józef Banaś

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

    Mohammad Mursaleen

Authors
  1. Józef Banaś
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  2. Mohammad Mursaleen
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Correspondence to Józef Banaś .

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Banaś, J., Mursaleen, M. (2014). Some Non-classical Sequence Spaces. In: Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1886-9_4

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