On some λ difference sequence spaces of fractional order

http://dx.doi.org/10.1016/j.joems.2016.06.005

Abstract

In the present paper, the difference sequence spaces csλ
0 (), csλ() and bsλ() of nonabsolute type are
generalized by introducing a generalized  difference operator ((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 p, c and c0 are characterized, where 1 ≤ p ≤ ∞.