Some new difference sequence spaces of λ-convergent and bounded series

In the study, we have studied; the difference sequence spaces csλ0(∆), csλ(∆) and bsλ(∆) of non-absolute type which is the domain of the difference matrix defined by Kızmaz (1981) on the sequence spaces csλ0, csλ and bsλ defined by Kaya and Furkan (2015) are defined and these sequence spaces are shown to be BK-spaces. Also, it is determined that these spaces are isomorphic to the spaces cs0, cs and bs, respectively, and their Schauder basis are given. In addition, some inclusion relations are examined and the α-, βand γ-duals of these sequence spaces are calculated. Finally, the classes of matrix transfor- mations from the spaces cs , csλ(∆) and bsλ(∆) to the spaces `p, c and c0 are characterized, where 1 6 p 6 ∞.