scholarly journals Difference sequence spaces

1998 ◽  
Vol 21 (4) ◽  
pp. 701-706 ◽  
Author(s):  
A. K. Gaur ◽  
Mursaleen
Keyword(s):  
Sequence Spaces ◽  
Difference Sequence ◽  
Matrix Classes ◽  
The Matrix ◽  
Difference Sequence Spaces

In [1]Sr(Δ):={x=(xk):(kr|Δxk|)k=1∞∈c0}forr≥1is studied. In this paper, we generalize this space toSr(p,Δ)for a sequence of strictly positive reals. We give a characterization of the matrix classes(Sr(p,Δ),ℓ∞)and(Sr(p,Δ),ℓ1).

On sequence spaces generated by binomial difference operator of fractional order

2019 ◽  
Vol 69 (4) ◽  
pp. 901-918 ◽  
Author(s):  
Taja Yaying ◽  
Bipan Hazarika
Keyword(s):  
Fractional Order ◽  
Hausdorff Measure ◽  
Difference Operator ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Fractional Difference ◽  
Matrix Classes ◽  
The Matrix ◽  
Difference Sequence Spaces

Abstract In this article we introduce binomial difference sequence spaces of fractional order α, $\begin{array}{} b_p^{r,s} \end{array}$ (Δ(α)) (1 ≤ p ≤ ∞) by the composition of binomial matrix, Br,s and fractional difference operator Δ(α), defined by (Δ(α)x)k = $\begin{array}{} \displaystyle \sum\limits_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i} \end{array}$. We give some topological properties, obtain the Schauder basis and determine the α, β and γ-duals of the spaces. We characterize the matrix classes ( $\begin{array}{} b_p^{r,s} \end{array}$(Δ(α)), Y), where Y ∈ {ℓ∞, c, c0, ℓ1} and certain classes of compact operators on the space $\begin{array}{} b_p^{r,s} \end{array}$(Δ(α)) using Hausdorff measure of non-compactness. Finally, we give some geometric properties of the space $\begin{array}{} b_p^{r,s} \end{array}$(Δ(α)) (1 < p < ∞).

scholarly journals On the generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

A SET OF NEW PARANORMED DIFFERENCE SEQUENCE SPACES AND THEIR MATRIX TRANSFORMATIONS

2013 ◽  
Vol 06 (03) ◽  
pp. 1350040 ◽  
Author(s):  
P. Baliarsingh
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Structures ◽  
The Matrix ◽  
The Difference ◽  
Positive Integers ◽  
Difference Sequence Spaces

In this paper, by using a new difference operator Δj, the author likes to introduce new classes of paranormed difference sequence spaces X(Δj, u, v; p) for X ∈ {ℓ∞, c, c0} and investigates their topological structures, where (un) and (vn) are two sequences satisfying certain conditions. The difference operator Δjis defined by Δj(xj) = jxj- (j + 1)xj+1for all j ∈ ℕ, the set of positive integers. Also, we determine the α-, β- and γ-duals of these classes. Furthermore, the matrix transformations from these classes to the sequence spaces ℓ∞(q), c0(q) and c(q) have been characterized.

scholarly journals Almost Sequence Spaces Derived by the Domain of the Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ali Karaisa ◽  
Ümıt Karabıyık
Keyword(s):  
Normed Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Classes ◽  
Almost Convergent Sequence ◽  
Inclusion Relations ◽  
The Matrix

By using , we introduce the sequence spaces , , and of normed space and -space and prove that , and are linearly isomorphic to the sequence spaces , , and , respectively. Further, we give some inclusion relations concerning the spaces , , and the nonexistence of Schauder basis of the spaces and is shown. Finally, we determine the - and -duals of the spaces and . Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.

On the space of p -summable difference sequences of order m , (1 ≦ p < ∞)

2006 ◽  
Vol 43 (4) ◽  
pp. 387-402 ◽  
Author(s):  
Bilâl Altay
Keyword(s):  
Sequence Space ◽  
Difference Sequence ◽  
Order Difference ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
The Matrix ◽  
The Difference ◽  
Matrix Mappings ◽  
Difference Sequence Spaces

The difference sequence spaces ℓ ∞ (Δ), c (Δ) and c0 (Δ) were studied by  Kizmaz [8]. The difference sequence space bvp , generated from the space ℓ p , has recently been introduced by Başar and Altay [5]. Several papers deal with the sets of sequences whose mth order difference are bounded, convergent or convergent to zero. The main purpose of the present paper is to introduce the space ℓ p (Δ (m) ) consisting of all sequences whose mth order differences are p -absolutely summable, and is to fill up the gap in the existing literature. Moreover, we give some topological properties and inclusion relations, a Schauder basis and determine the α-, β-, γ- and f- duals of the space ℓ p (Δ (m) ). The last section of the paper has been devoted to the characterization of the matrix mappings on the sequence space ℓ p (Δ (m) ).

scholarly journals On Some Classes of Double Difference Sequences of Interval Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Kuldip Raj ◽  
Abdullah Alotaibi
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Double Difference ◽  
Difference Sequence ◽  
Topological Properties ◽  
Interval Numbers ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Interval Valued ◽  
Difference Sequence Spaces

The aim of this paper is to introduce some interval valued double difference sequence spaces by means of Musielak-Orlicz functionM=(Mij). We also determine some topological properties and inclusion relations between these double difference sequence spaces.

scholarly journals On some generalized difference sequences with respect to a modulus function

Filomat ◽  
2003 ◽  
pp. 23-33 ◽  
Author(s):  
Mikail Et ◽  
Yavuz Altin ◽  
Hifsi Altinok
Keyword(s):  
Banach Space ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Colak [6]. In this paper we introduce the sequence spaces [V, ?, f, p]0 (?r, E), [V, ?, f, p]1 (?r, E), [V, ?, f, p]? (?r, E) S? (?r, E) and S?0 (?r, E) where E is any Banach space, examine them and give various properties and inclusion relations on these spaces. We also show that the space S? (?r, E) may be represented as a [V, ?, f, p]1 (?r, E)space.

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