Generalized difference sequence spaces defined by a sequence of moduli


Suzan Zeren, Çiğdem A. Bektaş




In this paper, we introduce and study the new sequence spaces $[V,\lambda ,F,p,q,u]_{0}\left( \Delta _{v}^{m}\right)$, $[V,\lambda,F,p,q,u]_{1}\left( \Delta _{v}^{m}\right)$ and $[V,\lambda,F,p,q,u]_{\infty }\left( \Delta _{v}^{m}\right)$ 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 topological properties of these spaces, and some inclusion relations between these spaces. This study generalizes results of Atıci and Bektaş [11].