On some new normed sequence spaces

Abstract

The sequence spaces (c 0)Λ, c Λ, and (ℓ ∞)Λ was introduced and studied by Mursaleen and Noman [11]. In the present paper, for M is a generalization of Orlicz function, we extend the spaces Mursaleen and Noman's to [c 0(M)]Λ, [c(M)]Λ, and [ℓ ∞(M)]Λ, respectively, and investigate some topological properties of these spaces. Finally, we determine the necessary and sufficient conditions of an infinite matrix A belonging to classes (c 0(M), c 0(M)), (c(M), c(M)), and (ℓ ∞(M), ℓ ∞(M)).