Some new type of difference sequence space of nonabsolute type and some matrix transformation

Abstract: In this paper, we introduce the space r q (
p u ), where r q (
p u ) = {x = (xk) ∈ ω : (uk
xj ) ∈ r q (u, p) < ∞} ; where r q (u, p) has recently been studied by Neyaz and Hamid. We show its completeness property, prove that the space r q (
p u ) and l(p) are linearly isomorphic and compute their α -, β- and γ-duals. Furthermore construct the basis of r q (u, p). In our last section we characterize some matrix class.