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) ).

On a class of difference sequences related to the ℓp space defined by Orlicz functions

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
Binod Tripathy ◽  
Sabita Mahanta
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Difference Sequence ◽  
Orlicz Functions ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
The Difference

AbstractIn this article we introduce the difference sequence space m(M, Δ, φ) using the Orlicz function. We study its different properties like solidity, completeness etc. Also we obtain some inclusion relations involving the space m(M, Δ, φ).

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.

scholarly journals Strongly almost convergent generalized difference sequences associated with multiplier sequences

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Ayhan Esi ◽  
Binod Tripathy
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Convergent Sequences

AbstractLet Λ = (λk) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e. w 0[A,Δm,Λ,p], w 1[A,Λm,Λ,p], w ∞[A,Δm,Λ,p] and study their different properties. We also introduce ΔΛm-statistically convergent sequences and give some inclusion relations between w 1[Δm,λ,p] convergence and ΔΛm-statistical convergence.

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 On the convergence difference sequences and the related operator norms

2020 ◽  
Vol 12 (2) ◽  
pp. 245-259
Author(s):  
P. Baliarsingh ◽  
L. Nayak ◽  
S. Samantaray
Keyword(s):  
Convergence Analysis ◽  
Fractional Order ◽  
Difference Operator ◽  
Difference Sequence ◽  
Primary Sequence ◽  
Fractional Difference ◽  
Difference Sequences ◽  
Operator Norms ◽  
The Difference ◽  
Difference Sequence Spaces

AbstractIn this note, we discuss the definitions of the difference sequences defined earlier by Kızmaz (1981), Et and Çolak (1995), Malkowsky et al. (2007), Başar (2012), Baliarsingh (2013, 2015) and many others. Several authors have defined the difference sequence spaces and studied their various properties. It is quite natural to analyze the convergence of the corresponding sequences. As a part of this work, a convergence analysis of difference sequence of fractional order defined earlier is presented. It is demonstrated that the convergence of the fractional difference sequence is dynamic in nature and some of the results involved are also inconsistent. We provide certain stronger conditions on the primary sequence and the results due to earlier authors are substantially modified. Some illustrative examples are provided for each point of the modifications. Results on certain operator norms related to the difference operator of fractional order are also determined.

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 some new generalized difference sequence spaces on seminormed spaces defined by a sequence of Orlicz functions

2011 ◽  
Vol 61 (2) ◽  
Author(s):  
Çiğdem Bektaş
Keyword(s):  
Linear Space ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Orlicz Functions ◽  
Inclusion Relations ◽  
Complex Linear ◽  
Difference Sequence Spaces

AbstractIn this paper we define the sequence space ℓ M(Δυm, p, q, s) on a seminormed complex linear space, by using a sequence of Orlicz functions. We study some algebraic and topological properties. We prove some inclusion relations involving ℓ M(Δυm, p, q, s). spaces

SOME DIFFERENCE SEQUENCE SPACES GENERATED BY DE LA VALLÉE-POUSSIN MEAN

2013 ◽  
Vol 06 (02) ◽  
pp. 1350018
Author(s):  
P. D. Srivastava ◽  
Atanu Manna
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Modular Structure ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
De La Vallée Poussin ◽  
Difference Sequence Spaces

A difference sequence space using φ-function and involving the concept of de la Vallée-Poussin mean is introduced. Inclusion relations, structural and topological properties of this space are investigated. By introducing a modular structure, the equality of the countably and uniformly countably modulared spaces is obtained.

scholarly journals On Vector-Valued Generalized Lorentz Difference Sequence Space

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Birsen Sağır ◽  
Oğuz Oğur
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
Vector Valued ◽  
Difference Sequence Spaces

We introduce generalized Lorentz difference sequence spaces d(v,Δ,p). Also we study some topologic properties of this space and obtain some inclusion relations.

Sign in / Sign up

Export Citation Format

Share Document