On Aλ -almost null and Aλ -almost convergent paranormed Orlicz sequence spaces

Abstract

The idea of almost convergent sequence was introduced by G. G. Lorentz [5]. In this paper, some new generalized sequence spaces on Aλ -almost null & 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)(Δ, M, q) : υ) & (υ : Aλ (f)(Δ, M, q)) of infinite matrices are also given.