On some λ difference sequence spaces of fractional order

In the present paper, the difference sequence spaces cs0λ(Δ),csλ(Δ) and bsλ(Δ) of nonabsolute type are generalized by introducing a generalized Λ difference operator Λ(Δ(α˜)). Also, their Schauder basis are calculated and α-, β- and γ-duals of these spaces are investigated. Finally, some matrix transformations between these spaces and the basic sequence spaces ℓp, c and c0 are characterized, where 1 ≤ p ≤ ∞.