On some Generalized Difference Sequence Spaces Defined by a Modulus Function


Mikâil Et, Yavuz Altin, Hifsi Altinok




The idea of difference sequence spaces was introduced by K\i zmaz [9] and generalized by Et and \c Colak [6]. In this paper we introduce the sequence spaces $[V,\lambda,f,p]_0(\Delta^r,E)$, $[V,\lambda,f,p]_1(\Delta^r,E)$, $[V,\lambda,f,p]_\infty(\Delta^r,E)$, $S_\lambda(\Delta^r,E)$ and $S_{\lambda_0}(\Delta^r,E)$, and where $E$ is any Banach space, examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_\lambda(\Delta^r,E)$ may be represented as a $[V,\lambda,f,p]_1(\Delta^r,E)$ space.