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Difference sequence spaces based on Lucas band matrix and modulus function

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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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Authors and Affiliations

  1. Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine

  2. Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine

  3. Department of Mathematics, Shri Mata Vaishno Devi University, Katra, 182320, Jammu and Kashmir, India

    Kuldip Raj & Anu Choudhary

Authors
  1. S. A. Mohiuddine
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  2. Kuldip Raj
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Correspondence to S. A. Mohiuddine.

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Communicated by H. M. Srivastava.

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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. 16, 1249–1260 (2022). https://doi.org/10.1007/s40863-020-00203-2

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