Generalized difference sequence spaces and their dual spaces

Abstract

The definition of the pα-, pβ-and pγ -duals of a sequence space was defined by Et [Internat. J. Math. Math. Sci. 24 (2000) 785-791]. In this paper we compute pα-and N-duals of the sequence spaces ∆ m v (X) for X = ∞ , c and c 0 , and compute β-and γ -duals of the sequence spaces ∆ m v (X) for X = ∞ , c and c 0 .  2004 Elsevier Inc. All rights reserved.

On some binomial B ( m ) $B^{(m)}$ -difference sequence spaces

“…Et and Colak [3] defined the generalization of the difference sequence spaces for , where , and for each , which is equivalent to the binomial representation . Since then, many authors have studied further generalization of the difference sequence spaces [4–7]. Moreover, Altay and Polat [8], Başarir and Kara [9–13], Başarir, Kara and Konca [14], Kara [15], Kara and İlkhan [16, 17], Polat and Başar [18], Song and Meng [19] and many others have studied new sequence spaces from matrix point of view that represent difference operators.…”

Some normed binomial difference sequence spaces related to the ℓ p $\ell_{p}$ spaces

“…Let Z be a sequence space, then Kizmaz [1] introduced the following difference sequence spaces: for , where for each , the set of positive integers. Since then, many authors have studied further generalization of the difference sequence spaces [2–6]. Moreover, Altay and Polat [7], Başarir and Kara [8–12], Kara [13], Kara and İlkhan [14], Polat and Başar [15], and many others have studied new sequence spaces from a matrix point of view that represent difference operators.…”

Euler-Ces`aro difference spaces of bounded, convergent and null sequences

“…which is a sequence space. By using the matrix domain of a triangle matrix, so many sequence spaces have recently been defined by several authors, see for instance [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. In the literature, the matrix domain λ ∆ is called the difference sequence space whenever λ is a normed or a paranormed sequence space, where ∆ denotes the backward difference matrix ∆ = (∆ nk ) and ∆ ′ = (∆ ′ nk ) denotes the transpose of the matrix ∆, the forward difference matrix, which are defined by…”