On the paranormed binomial sequence spaces

In this paper the sequence spaces b0r,s(p),bcr,s(p),b∞r,s(p) and br,s(p) which are the generalization of the classical Maddox’s paranormed sequence spaces have been introduced and proved that the spaces b0r,s(p),bcr,s(p),b∞r,s(p) and br,s(p) are linearly iso-morphic to spaces c0(p), c(p), ℓ∞(p) and ℓ(p), respectively. Besides this, the α-, β- and γ-duals of the spaces b0r,s(p),bcr,s, and br,s(p) have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices (b0r,s(p) : µ), (bcr,s(p) : µ) and (br,s(p) : µ) have been characterized, where µ is one of the sequence spaces ℓ∞, c and c0 and derives the other characterizations for the special cases of µ.