On the paranormed binomial sequence spaces

Abstract

In this paper the sequence spaces b(o)(r,s) (p), b(c)(r,s) (p), b(o)(r,s) (p) and b(o)(r,s) (p) which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces b(o)(r,s) (p), b(o)(r,s) (p), b(o)(r,s) Ap) and b(o)(r,s) (p) are linearly isomorphic to spaces co(p), c(p), too(p) and t(p), respectively. Besides this, the a,p and y duals of the spaces Yo' (p), b(o)(r,s) (p), and b"(p) have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices (b'cr (p) :), (bnp) :) and (b"(p) :) have been characterized, where is one of the sequence spaces t,s, c and co and derives the other characterizations for the special cases of p.