Difference sequence spaces based on Lucas band matrix and modulus function

Abstract

In this work, we define some difference sequence spaces based upon Lucas band matrix and associated with the idea of sequence of modulus functions and then establish that aforementioned spaces are BK-spaces of non absolute type.We further investigate that our spaces are linearly isomorphic to the space l(p), where \(l(p)=\{x=(x_{k}) \in w:\sum _{k}|x_{k}|^{p_{k}}<\infty \}\). Moreover, we demonstrate inclusion relationship between newly defined spaces as well as establish certain geometrical properties.

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Mohiuddine, S.A., Raj, K. & Choudhary, A. Difference sequence spaces based on Lucas band matrix and modulus function. São Paulo J. Math. Sci. (2021). https://doi.org/10.1007/s40863-020-00203-2

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Keywords

  • Lucas number
  • Modulus function
  • Weak fixed point property
  • Modulus of convexity
  • BK-spaces

Mathematics Subject Classification

  • 40A05
  • 40D25