On some generalized difference sequences with respect to a modulus function

The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Colak [6]. In this paper we introduce the sequence spaces [V, ?, f, p]0 (?r, E), [V, ?, f, p]1 (?r, E), [V, ?, f, p]? (?r, E) S? (?r, E) and S?0 (?r, E) 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? (?r, E) may be represented as a [V, ?, f, p]1 (?r, E)space.