The Generalized Difference Operator of Order Three and Its Domain in the Sequence Spaces e1 and bv

Tuğ, Orhan (2022) The Generalized Difference Operator of Order Three and Its Domain in the Sequence Spaces e1 and bv. Journal of Mathematics.

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Abstract

Most recently, the generalized difference operator Δ3 i of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ1(Δ3 i ) and bv(Δ3 i ) are introduced as the domain of generalized difference operator Δ3 i of order three in the sequence spaces ℓ1 and bv. +en, some topological properties of ℓ1(Δ3 i ) and bv(Δ3 i ) are given, and some inclusion relations are shown. Additionally, algebraic dual, α−, β−, and c− dual spaces of ℓ1(Δ3 i ) and bv(Δ3 i ) are computed. In the last section, the classes (μ(Δ3 i ): λ) and (λ: μ(Δ3 i )) of matrix transformations are characterized, where μ � ℓ1 � � , bv and λ � c, c0, ℓ1 � , ℓ∞, bs, cs, bv, h�.

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