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On some generalized difference sequences with respect to a modulus function

Et Mikail (Department of Mathematics, Firat University, Elazig, Turkey)
Altin Yavuz (Department of Mathematics, Firat University, Elazig, Turkey)
Altinok Hifsi (Department of Mathematics, Firat University, Elazig, Turkey)

The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Čolak [6]. In this paper we introduce the sequence spaces [V, λ, f, p]0 (Δr, E), [V, λ, f, p]1 (Δr, E), [V, λ, f, p]∞ (Δr, E) Sλ (Δr, E) and Sλ0 (Δr, 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 Sλ (Δr, E) may be represented as a [V, λ, f, p]1 (Δr, E)space.

Keywords: difference sequence, statistical convergence, modulus function