scholarly journals A New Double Sequence Space m2(F,ϕ,p) Defined by a Double Sequence of Modulus Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Birsen Sağır ◽  
Cenap Duyar ◽  
Oğuz Oğur
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Double Sequences ◽  
Double Sequence Space

In this work we introduce new spaces m2(F,ϕ,p) of double sequences defined by a double sequence of modulus functions, and we study some properties of this space.

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.

scholarly journals On a New Space of Double Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Cenap Duyar ◽  
Oğuz Oğur
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Double Sequence ◽  
Double Sequences ◽  
Double Sequence Space ◽  
Inclusion Relations ◽  
New Space

We introduce a new space of double sequences related to -absolute convergent double sequence space, combining an Orlicz function and an infinity double matrix. We study some properties of and obtain some inclusion relations involving .

scholarly journals Generalized vector valued double sequence space using modulus function

2007 ◽  
Vol 38 (4) ◽  
pp. 347-366
Author(s):  
Anindita Basu ◽  
P. D. Srivastava
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Double Sequence ◽  
Modulus Function ◽  
Real Numbers ◽  
Double Sequence Space ◽  
Seminormed Space ◽  
Vector Valued

In this paper, we introduce a generalized vector valued paranormed double sequence space $ F^{2}(E,p,f,s) $, using modulus function $ f $, where $ p=(p_{nk}) $ is a sequence of non-negative real numbers, $ s\geq 0 $ and the elements are chosen from a seminormed space $ (E, q_{E}) $. Results regarding completeness, normality, $ K_{2} $-space, co-ordinatewise convergence etc. are derived. Further, a study of multiplier sets, ideals, notion of statistical convergence and ($ p_{nk} $ )-Ces\'aro summability in the space $ F^{2}(E,p,f,s) $ is also made.

scholarly journals On Lacunary p-Absolutely Summable Fuzzy Real-Valued Double Sequence Space

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Amar Jyoti Dutta ◽  
Ayhan Esi ◽  
Binod Chandra Tripathy
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Double Sequence Space

AbstractIn this article, we introduce the class of p-absolutely summable fuzzy real valued double sequence (

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).

scholarly journals On a New I-Convergent Double-Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Vakeel A. Khan ◽  
Nazneen Khan
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Double Sequence Space ◽  
Inclusion Relations

The sequence space BVσ was introduced and studied by Mursaleen (1983). In this article we introduce the sequence space 2BVσI and study some of its properties and inclusion relations.

scholarly journals Double sequence transformations that guarantee a given rate of p-convergence

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 129-135 ◽  
Author(s):  
Richard Patterson ◽  
Ekrem Savaş
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Double Sequences ◽  
Dimensional Matrix ◽  
T Complex ◽  
Complex Sequences ◽  
Sequence Transformations

In this paper the following sequence space is presented. Let [t] be a positive double sequence and define the sequence space ?''(t) = {complex sequences x : xk,l = O(tk,l)}. The set of geometrically dominated double sequences is defined as G'' = U r,s?(0,1) G(r, s) where G(r, s) = {complex sequences x : x k,l = O(rk sl)} for each r, s in the interval (0, 1). Using this definition, four dimensional matrix characterizations of l?,?, c'', and c0'' into G'' and into ?''(t) are presented. In addition to these definitions and characterizations it should be noted that this ensure a rate of converges of at least as fast as [t]. Other natural implications will also be presented.

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 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.

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