SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz 13] studied the difference sequence spaces e∞(△), c(△), and c0(△).Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar 5] and Altay, Basar, and Mursaleen 7] introduced the Euler sequence spaces eτ0, eτ0, andeτ∞, respectively. The main purpose of this article is to introduce the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)) consisting of all sequences whose mth order differences are in the Euler spaces eτ0, eτc, and eτ∞, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)), and the Schauder basis of the spaces eτ0(△(m)), eτc(△(m)). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space eτc(△(m)).

Some Euler spaces of difference sequences of order m

Kizmaz 13] studied the difference sequence spaces ℓ_∞(Δ), c(Δ), and c0(Δ). Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Başar 5] and Altay, Başar, and Mursaleen 7] introduced the Euler sequence spaces e^r₀, e^r_c, and e^r_∞, respectively. The main purpose of this article is to introduce the spaces e^r₀(Δ^m), e^r_c(Δ^m), and e^r_∞(Δ^m) consisting of all sequences whose m^th order differences are in the Euler spaces e^r₀, e^r_c, and e^r_∞, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e^r₀(Δ^m), e^r_c(Δ^m), and e^r_∞(Δ^m), and the Schauder basis of the spaces e^r₀(Δ^m), e^r_c(Δ^m). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space e^r_c(Δ^m).