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Some Non-classical Sequence Spaces

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

Author

Listed:
  • Józef Banaś

    (Rzeszów University of Technology, Department of Mathematics)

  • Mohammad Mursaleen

    (Aligarh Muslim University, Department of Mathematics)

Abstract

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

Suggested Citation

  • Józef Banaś & Mohammad Mursaleen, 2014. "Some Non-classical Sequence Spaces," Springer Books, in: Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, edition 127, chapter 0, pages 105-146, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1886-9_4
    DOI: 10.1007/978-81-322-1886-9_4
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