Generalized difference sequence spaces defined by a sequence of moduli

Abstract

In this paper, we introduce and study the new sequence spaces [V,?,F,p,q,u]0 (? m v), [V;?,F,p,q,u]1 (? m v) and [V; ?,F,p,q,u]? (? m v) which are generalized difference sequence spaces defined by a sequence of moduli in a locally convex Haussdorff topological linear space X whose topology is determined by a finite set Q of continuous seminorms q. We also study various algebraic and topo-logical properties of these spaces, and some inclusion relations between these spaces. This study generalizes results of Atici and Bektaş [11].