scholarly journals ON GENERALIZED FIBONACCI DIFFERENCE SPACE DERIVED FROM THE ABSOLUTELY p− SUMMABLE SEQUENCE SPACES

2019 ◽  
pp. 903
Author(s):  
Gülsen Kılınç
Keyword(s):  
Sequence Space ◽  
Bounded Sequence ◽  
Sequence Spaces ◽  
The Other ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
Topological Features ◽  
Summable Sequence ◽  
Alpha Beta

In this study, it is specified \emph{the sequence space} $l\left( F\left( r,s\right),p\right) $, (where $p=\left( p_{k}\right) $ is any bounded sequence of positive real numbers) and researched some algebraic and topological features of this space. Further, $\alpha -,$ $\beta -,$ $\gamma -$ duals and its Schauder Basis are given. The classes of \emph{matrix transformations} from the space $l\left( F\left( r,s\right) ,p\right) $ to the spaces $l_{\infty },c,$ and $% c_{0}$ are qualified. Additionally, acquiring qualifications of some other \emph{matrix transformations} from the space $l\left( F\left( r,s\right) ,p\right) $ to the \emph{Euler, Riesz, difference}, etc., \emph{sequence spaces} is the other result of the paper.

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 Onk-nearly uniform convex property in generalized Cesàro sequence spaces

2003 ◽  
Vol 2003 (57) ◽  
pp. 3599-3607 ◽  
Author(s):  
Winate Sanhan ◽  
Suthep Suantai
Keyword(s):  
Sequence Space ◽  
Bounded Sequence ◽  
Sequence Spaces ◽  
Luxemburg Norm ◽  
Real Numbers ◽  
Positive Real ◽  
Generalized Cesáro Sequence Space ◽  
Convex Property

We define a generalized Cesàro sequence spaceces(p), wherep=(pk)is a bounded sequence of positive real numbers, and consider it equipped with the Luxemburg norm. The main purpose of this paper is to show thatces(p)isk-nearly uniform convex (k-NUC) fork≥2whenlimn→∞infpn>1. Moreover, we also obtain that the Cesàro sequence spacecesp(where 1<p<∞)isk-NUC,kR, NUC, and has a drop property.

scholarly journals Domain of the Double Sequential Band Matrix in the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Havva Nergiz ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Transformations ◽  
Difference Matrix ◽  
Band Matrix ◽  
Alpha Beta

The sequence space was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix in the sequence space has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space of nonabsolute type has been studied which is the domain of the generalized difference matrix in the sequence space . Furthermore, the alpha-, beta-, and gamma-duals of the space have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space to the spaces ,candc0have been characterized. Additionally, the characterizations of some other matrix transformations from the space to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.

scholarly journals Matrix transformations and application to perturbed problems of some sequence spaces equations with operators

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5123-5130
Author(s):  
Malafosse de ◽  
Ali Fares ◽  
Ali Ayad
Keyword(s):  
Linear Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
Complex Sequences ◽  
Perturbed Equation

Given any sequence z = (zn)n?1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n?1 such that y/z = (yn/zn)n?1 ? E; in particular, cz = s(c) z denotes the set of all sequences y such that y/z converges. Starting with the equation Fx = Fb we deal with some perturbed equation of the form ? + Fx = Fb, where ? is a linear space of sequences. In this way we solve the previous equation where ? =(Ea)T and (E,F) ? {(l?,c), (c0,l?), (c0,c), (lp,c), (lp,l?), (w0,l?)} with p ? 1, and T is a triangle.

scholarly journals On Some Properties of New Paranormed Sequence Space of Nonabsolute Type

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
The Other ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Paranormed Sequence Space ◽  
Inclusion Relations

We introduce some new generalized sequence space related to the space . Furthermore we investigate some topological properties as the completeness, the isomorphism, and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute -, -, and -duals of this space and characterize certain matrix transformations on this sequence space.

STRONGLY (VΛ,A,P) - SUMMABLE SEQUENCE SPACES DEFINED BY A MODULUS

2007 ◽  
Vol 12 (4) ◽  
pp. 419-424 ◽  
Author(s):  
Tunay Bilgin ◽  
Yilmaz Altun
Keyword(s):  
Key Words ◽  
Statistical Convergence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Real Numbers ◽  
Positive Real ◽  
Summable Sequence ◽  
De La Vallée Poussin

We introduce the strongly (Vλ,A,p) ‐ summable sequences and give the relation between the spaces of strongly (Vλ,A,p) ‐ summable sequences and strongly (Vλ,A,p) ‐ summable sequences with respect to a modulus function when A = (α ik ) is an infinite matrix of complex numbers and ρ = (pi) is a sequence of positive real numbers. Also we give natural relationship between strongly (Vλ, A,p) ‐ convergence with respect to a modulus function and strongly Sλ (A) ‐ statistical convergence. Key words: De la Vallee‐Poussin mean, modulus function, statistical convergence.

scholarly journals Mr-factors andQr-factors for near quasinorm on certain sequence spaces

2005 ◽  
Vol 2005 (15) ◽  
pp. 2441-2445
Author(s):  
Piyapong Niamsup ◽  
Yongwimon Lenbury
Keyword(s):  
Bounded Sequence ◽  
Sequence Spaces ◽  
Real Numbers ◽  
Positive Real

We study the multiplicativity factor and quadraticity factor for near quasinorm on certain sequence spaces of Maddox, namely,l(p)andl∞(p), wherep=(pk)is a bounded sequence of positive real numbers.

scholarly journals A new perspective on paranormed Riesz sequence space of non-absolute type

2015 ◽  
Vol 3 (4) ◽  
pp. 150 ◽  
Author(s):  
Murat Candan
Keyword(s):  
Sequence Space ◽  
Topological Properties ◽  
Real Numbers ◽  
Positive Real ◽  
Band Matrix ◽  
Current Article ◽  
Matrix Class ◽  
Alpha Beta ◽  
New Perspective ◽  
Convergent Sequences

<p>The current article mainly dwells on introducing Riesz sequence space \(r^{q}(\widetilde{B}_{u}^{p})\) which generalized the prior studies of Candan and Güneş [28], Candan and Kılınç [30]  and consists of all sequences whose \(R_{u}^{q}\widetilde{B}\)-transforms are in the space \(\ell(p)\), where \(\widetilde{B}=B(r_{n},s_{n})\) stands for double sequential band matrix \((r_{n})^{\infty}_{n=0}\) and \((s_{n})^{\infty}_{n=0}\) are given convergent sequences of positive real numbers. Some topological properties of the new brand sequence space have been investigated as well as \(\alpha\)- \(\beta\)-and \(\gamma\)-duals. Additionally, we have also constructed the basis of \(r^{q}(\widetilde{B}_{u}^{p})\). Eventually, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.</p>

scholarly journals On paranormed Ideal convergent sequence spaces defined by Jordan totient function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Vakeel A. Khan ◽  
Umme Tuba
Keyword(s):  
Law Of Large Numbers ◽  
Convergent Sequence ◽  
Decomposition Theorem ◽  
Bounded Sequence ◽  
Sequence Spaces ◽  
Usual Sense ◽  
Real Numbers ◽  
Positive Real ◽  
Large Numbers ◽  
Inclusion Relations

AbstractThe study of sequence spaces and summability theory has been an important aspect in defining new notions of convergence for the sequences that do not converge in the usual sense. Paving the way into the applications of law of large numbers and theory of functions, it has proved to be an essential tool. In this paper we generalise the classical Maddox sequence spaces $c_{0}(p)$ c 0 ( p ) , $c(p)$ c ( p ) , $\ell (p)$ ℓ ( p ) and $\ell _{\infty }(p)$ ℓ ∞ ( p ) and define new ideal paranormed sequence spaces $c^{I}_{0}(\Upsilon ^{r}, p)$ c 0 I ( ϒ r , p ) , $c^{I}(\Upsilon ^{r}, p)$ c I ( ϒ r , p ) , $\ell ^{I}_{ \infty }(\Upsilon ^{r}, p)$ ℓ ∞ I ( ϒ r , p ) and $\ell _{\infty }(\Upsilon ^{r}, p)$ ℓ ∞ ( ϒ r , p ) defined with the aid of Jordan’s totient function and a bounded sequence of positive real numbers. We develop isomorphism between certain maps and also find their α-, β- and γ-duals. We examine algebraic and topological properties of these corresponding spaces. Further we study some standard inclusion relations and prove the decomposition theorem.

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.

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