scholarly journals $f$-CONSERVATIVE MATRIX SEQUENCES

1991 ◽  
Vol 22 (2) ◽  
pp. 205-212
Author(s):  
FEYZI BASAR
Keyword(s):  
Matrix Classes ◽  
Matrix Sequence ◽  
The Matrix ◽  
Conservative Matrix

The main purpose of this paper is to determine the necessary and sufficint conditions on the matrix sequence $\mathcal{A} = (A_p)$ in order that $\mathcal{A}$ contained in one of the classes $(f: f)$, $(f :f_s)$, $(f_s: f)$ and $(f_s: f_s)$, where $f$ and $f_s$ respectively denote the spares of all almost convergent real sequences and series. Our results are more general than those of Duran [3] and Solak [7]. Additionally, theorems of Steinhaus type concerning some subclasses of above matrix classes, are also given.

scholarly journals A matrix sequence{Γ(Am)}m=1∞might converge even if the matrix A is not primitive

2013 ◽  
Vol 438 (5) ◽  
pp. 2306-2319 ◽  
Author(s):  
Woongbae Park ◽  
Boram Park ◽  
Suh-Ryung Kim
Keyword(s):  
Matrix Sequence ◽  
The Matrix

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

2016 ◽  
Vol 47 (4) ◽  
pp. 405-420 ◽  
Author(s):  
Feyzi Basar ◽  
Naim L. Braha
Keyword(s):  
Matrix Classes ◽  
Difference Sequences ◽  
The Matrix ◽  
Alpha Beta ◽  
Bk Spaces

In this paper, we introduce the spaces $\breve{\ell}_{\infty}$, $\breve{c}$ and $\breve{c}_{0}$ of Euler-Ces`aro bounded, convergent and null difference sequences and prove that the inclusions $\ell_{\infty}\subset\breve{\ell}_{\infty}$, $c\subset\breve{c}$ and $c_{0}\subset\breve{c}_{0}$ strictly hold. We show that the spaces $\breve{c}_{0}$ and $\breve{c}$ turn out to be the separable BK spaces such that $\breve{c}$ does not possess any of the following: AK property and monotonicity. We determine the alpha-, beta- and gamma-duals of the new spaces and characterize the matrix classes $(\breve{c}:\ell_{\infty})$, $(\breve{c}:c)$ and $(\breve{c}:c_0)$.  

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.

New characterizations of the matrix classes , and R0

2021 ◽  
Vol 621 ◽  
pp. 181-192
Author(s):  
S.M. Miri ◽  
S. Effati
Keyword(s):  
Matrix Classes ◽  
The Matrix

scholarly journals Matrix transformations of strongly convergent sequences into Vσ

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 103-109 ◽  
Author(s):  
S.A. Mohiuddine ◽  
M. Aiyub
Keyword(s):  
Matrix Transformations ◽  
Matrix Classes ◽  
The Matrix ◽  
Bounded Sequences ◽  
Convergent Sequences

In this paper, we define the spaces ?(p, s) and ?p (s), where ?(p, s) = {x:1/n? k=1 K-s |xk -?|pk ? 0 for some ?, s ? 0} and if pk = p for each k, we have ?(p, s)=?p(s). We further characterize the matrix classes (?(p, s), V? ), (?p (s), V? ) and (?p (s), V? )reg , where V? denotes the set of bounded sequences all of whose ?-mean are equal.

scholarly journals Matrix Representation of Bi-Periodic Jacobsthal Sequence

2020 ◽  
pp. 1-12
Author(s):  
Sukran Uygun ◽  
Evans Owusu
Keyword(s):  
Generating Function ◽  
Initial Conditions ◽  
Matrix Representation ◽  
General Term ◽  
Identity Matrix ◽  
Summation Formulas ◽  
Matrix Sequence ◽  
Binet Formula ◽  
The Matrix ◽  
Generalized Matrix

In this paper, we bring into light the matrix representation of bi-periodic Jacobsthal sequence, which we shall call the bi-periodic Jacobsthal matrix sequence. We dene it as with initial conditions J0 = I identity matrix, . We obtained the nth general term of this new matrix sequence. By studying the properties of this new matrix sequence, the well-known Cassini or Simpson's formula was obtained. We then proceed to find its generating function as well as the Binet formula. Some new properties and two summation formulas for this new generalized matrix sequence were also given.

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).

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