on aλ-almost null and aλ-almost convergent orlicz sequence spaces

The idea of almost convergent sequence was introduced by g. g. lorentz [8]. in this paper, some new generalized sequence spaces on aλ-almost null and aλ-almost convergent sequences by orlicz function are introduced and extended them to the paranormed sequence spaces. some inclusion relation has also been established between the new spaces. in addition, the α-, β- and γ-duals of these spaces, and the characterization of (aλ(f)(∆, m, q) : ν) and (ν : aλ(f)(∆, m, q)) of infinite matrices are also given.