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 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).

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 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 matrix transformations concerning the Nakano vector-valued sequence space

2001 ◽  
Vol 26 (11) ◽  
pp. 671-678
Author(s):  
Suthep Suantai
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
The Matrix ◽  
Vector Valued ◽  
Bounded Sequences

We give the matrix characterizations from Nakano vector-valued sequence spaceℓ(X,p)andFr(X,p)into the sequence spacesEr,ℓ∞,ℓ¯∞(q),bs, andcs, wherep=(pk)andq=(qk)are bounded sequences of positive real numbers such thatPk>1for allk∈ℕandr≥0.

scholarly journals On Some I-Convergent Double Sequence Spaces of Fuzzy Real Numbers Defined by Modulus Function

2015 ◽  
Vol 55 (1) ◽  
pp. 19-28
Author(s):  
Manmohan Das
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Real Numbers ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties ◽  
Fuzzy Real Numbers

Abstract In this article our aim to introduce some new I-convergent double sequence spaces of fuzzy real numbers defined by modulus function and studies their some topological and algebraic properties. Also we establish some inclusion relations.

scholarly journals Different types of quasi-weighted αβ-statistical convergence in probability

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1463-1473 ◽  
Author(s):  
Pratulananda Das ◽  
Sanjoy Ghosal ◽  
Sumit Som
Keyword(s):  
Probability Distribution ◽  
Statistical Convergence ◽  
Random Variable ◽  
Convergence In Probability ◽  
Modulus Function ◽  
Real Numbers ◽  
Related Concept ◽  
Different Types ◽  
Weighted Modulus ◽  
Relational Behavior

The sequence of random variables {Xn}n?N is said to be weighted modulus ??-statistically convergent in probability to a random variable X [16] if for any ?,? > 0, limn??1 1/T??(n) |{k ? T??(n): tk?(P(|Xk-X|? ?)) ? ?}| = 0 where ? be a modulus function and {tn}n?N be a sequence of real numbers such that limn?? inf tn > 0 and T??(n) = ? k?[?n,?n] tk ? n ? N. In this paper we study a related concept of convergence in which the value 1/ T??(n) is replaced by 1/Cn, for some sequence of real numbers {Cn}n?N such that Cn > 0 8 n ? N, lim n?1 Cn = ? and lim n?1 sup Cn T??(n)< 1 (like [30]). The results are applied to build the probability distribution for quasi-weighted modulus ??-statistical convergence in probability, quasi-weighted modulus ??-strongly Ces?ro convergence in probability, quasi-weighted modulus S??-convergence in probability and quasiweighted modulus N??-convergence in probability. If {Cn}n?N satisfying the condition lim n?1 inf Cn/T??(n) > 0, then quasi-weighted modulus ??-statistical convergence in probability and weighted modulus ??-statistical convergence in probability are equivalent except the condition lim n?1 inf Cn T??(n) = 0. So our main objective is to interpret the above exceptional condition and produce a relational behavior of above mention four convergences.

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