Domain of the double sequential band matrix B() on some maddox's spaces

The domain of generalized difference matrix B(r, s) in the classical spaces ℓ∞, c, and c0 was recently studied by Kirişçi and Başar in [16]. The main goal of this article is to introduce the paranormed sequence spaces ℓ∞(), c(), and c0(), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces ℓ∞(), c(), and c0() are computed and the bases of the spaces c() and c0() are constructed. The final section of this article is devoted to the characterization of the classes (λ() : μ) and (μ : λ()), where λ ∈ {c, c0, ℓ∞} and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.