scholarly journals On the Zweier Sequence Spaces of Fuzzy Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mehmet Şengönül
Keyword(s):  
Sequence Space ◽  
Fuzzy Numbers ◽  
Sequence Spaces ◽  
Matrix Domain ◽  
The Matrix ◽  
Limitation Method

It was given a prototype constructing a new sequence space of fuzzy numbers by means of the matrix domain of a particular limitation method. That is we have constructed the Zweier sequence spaces of fuzzy numbers[ℓ∞(F)]Zη,[c(F)]Zη, and[c0(F)]Zηconsisting of all sequencesu=(uk)such thatZηuin the spacesℓ∞(F),c(F), andc0(F), respectively. Also, we prove that[ℓ∞(F)]Zη,[c(F)]Zη, and[c0(F)]Zηare linearly isomorphic to the spacesℓ∞(F),c(F), andc0(F), respectively. Additionally, theα(r)-,β(r)-, andγ(r)-duals of the spaces[ℓ∞(F)]Zη,[c(F)]Zη, and[c0(F)]Zηhave been computed. Furthermore, two theorems concerning matrix map have been given.

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 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 New matrix domain derived by the matrix product

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1233-1241
Author(s):  
Vatan Karakaya ◽  
Necip Imşek ◽  
Kadri Doğan
Keyword(s):  
Topological Structure ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Matrix Product ◽  
Difference Matrix ◽  
Matrix Domain ◽  
The Matrix ◽  
Necessary And Sufficient

In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the ?-, ?- and ?- duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c,??.

scholarly journals A study on Copson operator and its associated sequence space II

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Domains

AbstractIn this paper, we investigate some properties of the domains $c(C^{n})$ c ( C n ) , $c_{0}(C^{n})$ c 0 ( C n ) , and $\ell _{p}(C^{n})$ ℓ p ( C n ) $(0< p<1)$ ( 0 < p < 1 ) of the Copson matrix of order n, where c, $c_{0}$ c 0 , and $\ell _{p}$ ℓ p are the spaces of all convergent, convergent to zero, and p-summable real sequences, respectively. Moreover, we compute the Köthe duals of these spaces and the lower bound of well-known operators on these sequence spaces. The domain $\ell _{p}(C^{n})$ ℓ p ( C n ) of Copson matrix $C^{n}$ C n of order n in the sequence space $\ell _{p}$ ℓ p , the norm of operators on this space, and the norm of Copson operator on several matrix domains have been investigated recently in (Roopaei in J. Inequal. Appl. 2020:120, 2020), and the present study is a complement of our previous research.

scholarly journals Dual pairs of sequence spaces

2001 ◽  
Vol 28 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Johann Boos ◽  
Toivo Leiger
Keyword(s):  
Sequence Space ◽  
Dual Pair ◽  
General Concept ◽  
Sequence Spaces ◽  
Dual Pairs ◽  
The Third ◽  
Convex Sequence ◽  
Starting Point ◽  
Alpha Beta ◽  
Locally Convex

The paper aims to develop for sequence spacesEa general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz dualsE×(×∈{α,β})combined with dualities(E,G),G⊂E×, and theSAK-property (weak sectional convergence). TakingEβ:={(yk)∈ω:=𝕜ℕ|(ykxk)∈cs}=:Ecs, wherecsdenotes the set of all summable sequences, as a starting point, then we get a general substitute ofEcsby replacingcsby any locally convex sequence spaceSwith sums∈S′(in particular, a sum space) as defined by Ruckle (1970). This idea provides a dual pair(E,ES)of sequence spaces and gives rise for a generalization of the solid topology and for the investigation of the continuity of quasi-matrix maps relative to topologies of the duality(E,Eβ). That research is the basis for general versions of three types of inclusion theorems: two of them are originally due to Bennett and Kalton (1973) and generalized by the authors (see Boos and Leiger (1993 and 1997)), and the third was done by Große-Erdmann (1992). Finally, the generalizations, carried out in this paper, are justified by four applications with results around different kinds of Köthe-Toeplitz duals and related section properties.

Some criteria for nuclearity

1986 ◽  
Vol 100 (1) ◽  
pp. 151-159 ◽  
Author(s):  
M. A. Sofi
Keyword(s):  
Sequence Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Sequence Spaces ◽  
Bilinear Forms ◽  
Simple Formulation ◽  
Normal Topology ◽  
Nuclear Spaces ◽  
Locally Convex

For a given locally convex space, it is always of interest to find conditions for its nuclearity. Well known results of this kind – by now already familiar – involve the use of tensor products, diametral dimension, bilinear forms, generalized sequence spaces and a host of other devices for the characterization of nuclear spaces (see [9]). However, it turns out, these nuclearity criteria are amenable to a particularly simple formulation in the setting of certain sequence spaces; an elegant example is provided by the so-called Grothendieck–Pietsch (GP, for short) criterion for nuclearity of a sequence space (in its normal topology) in terms of the summability of certain numerical sequences.

Upper lp-estimates in vector sequence spaces, with some applications

1993 ◽  
Vol 113 (2) ◽  
pp. 329-334 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Fernando Sánchez
Keyword(s):  
Banach Spaces ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Vector Sequence ◽  
Lp Estimates ◽  
Banach Sequence Space ◽  
Banach Sequence

In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers

2016 ◽  
Vol 33 (06) ◽  
pp. 1650047 ◽  
Author(s):  
Sanjiv Kumar ◽  
Ritika Chopra ◽  
Ratnesh R. Saxena
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Linear Programming ◽  
Matrix Game ◽  
Matrix Games ◽  
Trapezoidal Fuzzy Numbers ◽  
Fast Approach ◽  
The Matrix

The aim of this paper is to develop an effective method for solving matrix game with payoffs of trapezoidal fuzzy numbers (TrFNs). The method always assures that players’ gain-floor and loss-ceiling have a common TrFN-type fuzzy value and hereby any matrix game with payoffs of TrFNs has a TrFN-type fuzzy value. The matrix game is first converted to a fuzzy linear programming problem, which is converted to three different optimization problems, which are then solved to get the optimum value of the game. The proposed method has an edge over other method as this focuses only on matrix games with payoff element as symmetric trapezoidal fuzzy number, which might not always be the case. A numerical example is given to illustrate the method.

scholarly journals On rough convergence of triple sequence space of Bernstein operator of fuzzy numbers defined by a metric

2020 ◽  
Vol 39 (2) ◽  
pp. 261-274
Author(s):  
M. Jeyaram Bharathi ◽  
S. Velmurugan ◽  
N. Subramanian ◽  
R. Srikanth
Keyword(s):  
Sequence Space ◽  
Fuzzy Numbers ◽  
Bernstein Operator
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