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.

scholarly journals The application domain of difference type matrix D(r,0,s,0,t) on some sequence spaces

2020 ◽  
pp. 32-32
Author(s):  
Avinoy Paul ◽  
Binod Tripathy
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Application Domain ◽  
Topological Properties ◽  
Difference Type ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper we introduce new sequence spaces with the help of domain of matrix D(r,0,s,0,t), and study some of their topological properties. Further, we determine ? and ? duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of the matrix mappings.

scholarly journals Measures of noncompactness in (N¯qΔ)summable difference sequence spaces

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5459-5470
Author(s):  
Ishfaq Malik ◽  
Tanweer Jalal
Keyword(s):  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Hausdorff Measure Of Noncompactness ◽  
Measures Of Noncompactness ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper we first introduce N?q?summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices A to map these sequence spaces into the spaces c,c0, and l?. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

scholarly journals On some new paranormed sequence spaces defined by the matrix (D )(r,0,0,s)

2021 ◽  
Vol 40 (3) ◽  
pp. 779-796
Author(s):  
Avinoy Paul
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Topological Properties ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper, we introduce some new paranormed sequence spaces and study some topological properties. Further, we determine α, β and γ-duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of matrix mappings.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

2021 ◽  
Vol 71 (6) ◽  
pp. 1375-1400
Author(s):  
Feyzi Başar ◽  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
The Matrix ◽  
Alpha Beta ◽  
Necessary And Sufficient ◽  
Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

scholarly journals A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

1995 ◽  
Vol 18 (4) ◽  
pp. 681-688 ◽  
Author(s):  
B. Choudhary ◽  
S. K. Mishra
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Necessary And Sufficient

In this paper we define the sequence spacesSℓ∞(p),Sc(p)andSc0(p)and determine the Köthe-Toeplitz duals ofSℓ∞(p). We also obtain necessary and sufficient conditions for a matrixAto mapSℓ∞(p)toℓ∞and investigate some related problems.

scholarly journals Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Uğur Kadak ◽  
Hakan Efe
Keyword(s):  
Linear Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
General Linear ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
Complex Field ◽  
Infinite Matrices ◽  
The Matrix ◽  
Necessary And Sufficient

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the fieldC*and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets overC*to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples.

On generalized Fibonacci difference sequence spaces and compact operators

2021 ◽  
pp. 2250116
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Mikail Et
Keyword(s):  
Fractional Order ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Band Matrix ◽  
Matrix Formula ◽  
Necessary And Sufficient ◽  
Matrix Mappings ◽  
Difference Sequence Spaces

In this paper, we introduce Fibonacci backward difference operator [Formula: see text] of fractional order [Formula: see text] by the composition of Fibonacci band matrix [Formula: see text] and difference operator [Formula: see text] of fractional order [Formula: see text] defined by [Formula: see text] and introduce sequence spaces [Formula: see text] and [Formula: see text] We present some topological properties, obtain Schauder basis and determine [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the spaces [Formula: see text] and [Formula: see text] We characterize certain classes of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to any of the space [Formula: see text] [Formula: see text] [Formula: see text] or [Formula: see text] Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces [Formula: see text] and [Formula: see text]

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 New matrix domain derived by the matrix product

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1233-1241
Author(s):  
Vatan Karakaya ◽  
Necip Imşek ◽  
Kadri Doğan
Keyword(s):  
Topological Structure ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Matrix Product ◽  
Difference Matrix ◽  
Matrix Domain ◽  
The Matrix ◽  
Necessary And Sufficient

In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the ?-, ?- and ?- duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c,??.

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 < ∞).

Sign in / Sign up

Export Citation Format

Share Document