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The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv

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  • Orhan Tuğ

Abstract

Most recently, the generalized difference operator Δi3 of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ1Δi3 and bvΔi3 are introduced as the domain of generalized difference operator Δi3 of order three in the sequence spaces ℓ1 and bv. Then, some topological properties of ℓ1Δi3 and bvΔi3 are given, and some inclusion relations are shown. Additionally, algebraic dual, α−, β−, and γ− dual spaces of ℓ1Δi3 and bvΔi3 are computed. In the last section, the classes μΔi3:λ and λ:μΔi3 of matrix transformations are characterized, where μ = {ℓ1, bv} and λ = {c, c0, ℓ1, ℓ∞, bs, cs, bv, h}.

Suggested Citation

  • Orhan Tuğ, 2022. "The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6343084
    DOI: 10.1155/2022/6343084
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    References listed on IDEAS

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    1. A. K. Gaur & Mursaleen, 1998. "Difference sequence spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 21, pages 1-6, January.
    2. Baliarsingh, P. & Dutta, S., 2015. "On the classes of fractional order difference sequence spaces and their matrix transformations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 665-674.
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