Domain of generalized difference operator Δi³ of order three on the hahn sequence space h and matrix transformations.

In this article, domain of the third order generalized difference operator Δ_i³ in Hahn sequence space h is introduced. Some topological properties and inclusion relations are shown. Additionally, Schauder basis of the new Hahn sequence space h(Δ_i³) is calculated and α-, β- and γ-dual of the space h(Δ_i³) are computed. In the last section, some new matrix classes (h; bv), (h; bv_p), (h; bv_∞), (h; bs), (h; cs), (bv; h), (bv0; h), (bs; h), (cs₀; h), (cs; h) are characterized. We conclude the paper with characterization of the classes (h(Δ_i³); μ) and (μ; h(Δ_i³)) where μ = {c, c₀, l₁, l_p, l_∞, h, bs, cs, cs₀, bv, bv₀}. [ABSTRACT FROM AUTHOR]