scholarly journals Matrix summability of statistically p-convergence sequences

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 55-62 ◽  
Author(s):  
Richard Patterson ◽  
Ekrem Savaş
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Arbitrary Sequence ◽  
Regular Matrix ◽  
Multidimensional Analog ◽  
Matrix Summability ◽  
Double Sequence Spaces ◽  
Double Sequence Space

Matrix summability is arguable the most important tool used to characterize sequence spaces. In 1993 Kolk presented such a characterization for statistically convergent sequence space using nonnegative regular matrix. The goal of this paper is extended Kolk?s results to double sequence spaces via four dimensional matrix transformation. To accomplish this goal we begin by presenting the following multidimensional analog of Kolk?s Theorem : Let X be a section-closed double sequence space containing e'' and Y an arbitrary sequence space. Then B ?(st2A ? X,Y) if and only if B ? (c''? X,Y) and B[KxK]?(X,Y) (?A(K?K)=0). In addition, to this result we shall also present implication and variation of this theorem.

scholarly journals On double sequence spaces defined by an Orlicz function on a seminormed space

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 631-638 ◽  
Author(s):  
Ekrem Savaş ◽  
Eren Savaş
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequence Spaces ◽  
Double Sequence Space ◽  
Seminormed Space ◽  
Inclusion Results

In this paper we introduce and study the double sequence space m''(M,?,q) by using the Orlicz function M. Also we obtain some inclusion results involving the space m''(M,?,q).

Almost strongly Orlicz double sequence spaces of regular matrices and their applications to statistical convergence

2018 ◽  
Vol 11 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Kuldip Raj ◽  
Anu Choudhary ◽  
Charu Sharma
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Regular Matrix ◽  
Normed Spaces ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over [Formula: see text]-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over [Formula: see text]-normed spaces.

scholarly journals Some Almost Lacunary Double Sequence Spaces Defined by Orlicz Functions in 2-Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Normed Spaces ◽  
Orlicz Functions ◽  
Double Sequence Spaces ◽  
Almost Convergent Sequence

Das and Patel (1989) introduced two new sequence spaces which are called lacunary almost convergent and lacunary strongly almost convergent sequence spaces. Móricz and Rhoades (1988) defined and studied almost P-convergent double sequences spaces. Savaş and Patterson (2005) introduce the almost lacunary strong P-convergent double sequence spaces by using Orlicz functions and examined some properties of these sequences spaces. In this paper, some almost lacunary double sequences spaces are given by using 2-normed spaces.

scholarly journals On strong double matrix summability via ideals

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1143-1150 ◽  
Author(s):  
Ekrem Savaş
Keyword(s):  
Orlicz Function ◽  
Double Sequence ◽  
Summability Method ◽  
Sequence Spaces ◽  
Matrix Summability ◽  
Double Sequence Spaces ◽  
Dimensional Matrix

In this paper, we define some new double sequence spaces by combining the notion of ideal, Orlicz function and nonnegative four dimensional matrix. We make certain investigations on the classes of sequences arising out of this new summability method. In addition, we shall establish inclusion theorems between these spaces and other sequence spaces.

scholarly journals On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 789
Author(s):  
Orhan Tuğ ◽  
Vladimir Rakočević ◽  
Eberhard Malkowsky
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Double Sequences ◽  
Real Numbers ◽  
Band Matrix ◽  
Double Sequence Spaces ◽  
Double Sequence Space ◽  
Inclusion Relations ◽  
Matrix Mappings

Let E represent any of the spaces M u , C ϑ ( ϑ = { b , b p , r } ) , and L q ( 0 < q < ∞ ) of bounded, ϑ -convergent, and q-absolutely summable double sequences, respectively, and E ˜ be the domain of the four-dimensional (4D) infinite sequential band matrix B ( r ˜ , s ˜ , t ˜ , u ˜ ) in the double sequence space E, where r ˜ = ( r m ) m = 0 ∞ , s ˜ = ( s m ) m = 0 ∞ , t ˜ = ( t n ) n = 0 ∞ , and u ˜ = ( u n ) n = 0 ∞ are given sequences of real numbers in the set c ∖ c 0 . In this paper, we investigate the double sequence spaces E ˜ . First, we determine some topological properties and prove several inclusion relations under some strict conditions. Then, we examine α -, β ( ϑ ) -, and γ -duals of E ˜ . Finally, we characterize some new classes of 4D matrix mappings related to our new double sequence spaces and conclude the paper with some significant consequences.

scholarly journals Properties of $\Gamma^{2}$ defined by a modulus function

2012 ◽  
Vol 31 (1) ◽  
pp. 193
Author(s):  
Chinnswamy Murugesan ◽  
Nagarajan Subramanian
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Double Sequence Spaces

In this article, we introduces the generalized difference paranormed double sequence spaces $\Gamma^{2}\left(\Delta^{m}_{\gamma},f,p,q,s\right)$ and $\Lambda^{2} \left(\Delta^{m}_{\gamma},f,p,q,s\right)$ defined over a seminormed sequence space  $\left(X,q\right)$

scholarly journals A New RH-Regular Matrix Derived by Jordan’s Function and Its Domains on Some Double Sequence Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sezer Erdem ◽  
Serkan Demiriz
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Regular Matrix ◽  
Double Sequence Spaces ◽  
Dimensional Matrix

In the present study, we introduce a new RH-regular 4D (4-dimensional) matrix derived by Jordan’s function and define double sequence spaces by using domains of 4D Jordan totient matrix J t on some classical double sequence spaces. Also, the α -, β ϑ -, and γ -duals of these spaces are determined. Finally, some classes of 4D matrices on these spaces are characterized.

On the domain of Riesz mean in the space Ls

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 925-940 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Riesz Mean ◽  
Double Sequence Space ◽  
Necessary And Sufficient ◽  
Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

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