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.

scholarly journals Almost convergent sequence spaces derived by the domain of quadruple band matrix

2020 ◽  
Vol 19 (1) ◽  
pp. 155-170
Author(s):  
Mustafa Cemil Bişgin
Keyword(s):  
Convergent Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Third Order ◽  
Difference Matrix ◽  
Order Difference ◽  
Matrix Classes ◽  
Band Matrix ◽  
Almost Convergent Sequence ◽  
Triple Band

AbstractIn this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ3, B(r, s, t), Δ2, B(r, s) and Δ, where Δ3, B(r, s, t), Δ2, B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

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).

SOME ALMOST CONVERGENT SEQUENCE SPACES OF FUZZY NUMBERS GENERATED BY INFINITE MATRICES

2006 ◽  
Vol 02 (02) ◽  
pp. 115-121
Author(s):  
EKREM SAVAS
Keyword(s):  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Infinite Matrices ◽  
Almost Convergent Sequence ◽  
Inclusion Relations

In this paper we define some almost convergent sequence spaces of fuzzy numbers by using the A-transforms and we also examine topological properties and some inclusion relations for these new sequence spaces.

On sequence spaces defined by the domain of a regular tribonacci matrix

2020 ◽  
Vol 70 (3) ◽  
pp. 697-706 ◽  
Author(s):  
Taja Yaying ◽  
Bipan Hazarika
Keyword(s):  
Sequence Spaces ◽  
Schauder Basis ◽  
Topological Properties ◽  
Inclusion Relation ◽  
Geometric Properties ◽  
Matrix Classes ◽  
The Matrix

AbstractIn this article we introduce Tribonacci sequence spaces ℓp(T) (1 ≤ p ≤ ∞) derived by the domain of a newly defined regular Tribonacci matrix. We give some topological properties, inclusion relation, obtain the Schauder basis and determine the α-, β- and γ-duals of the new spaces. We characterize the matrix classes on ℓp(T). Finally, we give some geometric properties of the space ℓp(T).

scholarly journals On Domain of Nörlund Sequences

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 268 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Fevzi Yaşar
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Sequence Space ◽  
Convergent Series ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Nörlund Matrix ◽  
Inclusion Relations ◽  
The Matrix ◽  
New Space

In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α­, β­, γ­duals, and characterized their matrix transformations on this space and into this space.

scholarly journals On the Characterization of Some Classes of Four-Dimensional Matrices and Almost B-Summable Double Sequences

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Matrix Classes ◽  
Related Literature ◽  
Double Sequence Spaces

We firstly summarize the related literature about Br,s,t,u-summability of double sequence spaces and almost Br,s,t,u-summable double sequence spaces. Then we characterize some new matrix classes of Ls′:Cf, BLs′:Cf, and Ls′:BCf of four-dimensional matrices in both cases of 0<s′≤1 and 1<s′<∞, and we complete this work with some significant results.

scholarly journals On statistical convergent sequence spaces of intuitionistic Fuzzy numbers

2018 ◽  
Vol 36 (1) ◽  
pp. 235 ◽  
Author(s):  
Shyamal Debnath ◽  
Vishnu Narayan Mishra ◽  
Jayanta Debnath
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Inclusion Relations ◽  
Bounded Sequences

In the present paper we introduce the classes of sequence stcIFN, stc0IFN and st∞IFN of statistically convergent, statistically null and statistically bounded sequences of intuitionistic fuzzy number based on the newly defined metric on the space of all intuitionistic fuzzy numbers (IFNs). We study some algebraic and topological properties of these spaces and prove some inclusion relations too.

scholarly journals Some Results on Strongly Cesáro Ideal Convergent Sequence Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Mohammad Faisal Khan
Keyword(s):  
Convergent Sequence ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

Some algebraic properties of Cesáro ideal convergent sequence spaces, C I and C 0 I , are studied in this article and some inclusion relations on these spaces are established.

scholarly journals New Difference Sequence Spaces Defined by Musielak-Orlicz Function

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
S. A. Mohiuddine ◽  
A. Kılıçman
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce new sequence spaces by using Musielak-Orlicz function and a generalizedB∧ μ-difference operator onn-normed space. Some topological properties and inclusion relations are also examined.

Sign in / Sign up

Export Citation Format

Share Document