Communications of the
Korean Mathematical Society CKMS

In this paper, we define the sequence spaces: {\small $% [V,\lambda ,f,$ $p]_0(\Delta ^r,E,u),$ $[V,\lambda ,f,p]_1(\Delta ^r,E,u),\, [V,\lambda ,f,p]_\infty (\Delta ^r,E,u),\, S_{_\lambda }$ {\linebreak}$(\Delta ^r,E,u),$} and $S_{\lambda 0}(\Delta ^r,E,u),$ where $E$ is any Banach space, and $u=(u_k)$ be any sequence such that $u_k\neq 0$ for any $k$ , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{_\lambda }(\Delta ^r,E,u)$ may be represented as a $[V,\lambda ,f,p]_1(\Delta ^r,E,u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

Keywords: difference sequence, statistical convergence, modulus function

MSC numbers: 40A05, 40C05, 46A45