some topological and geometrical properties of a new difference sequence space

We introduce the new difference sequence space 𝑎𝑟𝑝(Δ) . Further, it is proved that the space 𝑎𝑟𝑝(Δ) is the BK-space including the space 𝑏𝑣𝑝, which is the space of sequences of pbounded variation. We also show that the spaces 𝑎𝑟𝑝(Δ), and ℓ𝑝 are linearly isomorphic for 1≤𝑝<∞. Furthermore, the basis and the 𝛼-, 𝛽- and 𝛾-duals of the space 𝑎𝑟𝑝(Δ) are determined. We devote the final section of the paper to examine some geometric properties of the space 𝑎𝑟𝑝(Δ).