On the paranormed binomial sequence spaces

Abstract

In this paper the sequence spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p) which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p) are linearly isomorphic to spaces c 0 (p), c(p), ∞ (p) and (p), respectively. Besides this, the α−, β − and γ−duals of the spaces b r,s 0 (p), b r,s c (p), and b r,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 (b r,s 0 (p) : µ), (b r,s c (p) : µ) and (b r,s (p) : µ) have been characterized, where µ is one of the sequence spaces ∞ , c and c 0 and derives the other characterizations for the special cases of µ.

On the paranormed binomial sequence spaces

“…Also, we have constructed the basis and computed the α−, β − and γ−duals and investigated some topological properties of the spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p). Following Choudhary and Mishra [7], Başar and Altay [3], Altay and Başar [1,2], Demiriz [8], Kirişçi [14,15], Candan and Güneş [16] and Ellidokuzoglu and Demiriz [9], we define the sequence spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p), as the sets of all sequences such that B r,s −transforms of them are in the spaces c 0 (p), c(p), ∞ (p) and (p), respectively, that is,…”