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 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 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 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 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 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 A new type of paranorm intuitionistic fuzzy Zweier I-convergent double sequence spaces

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1279-1286 ◽  
Author(s):  
Vakeel Khan ◽  
Y Yasmeen ◽  
Hira Fatima ◽  
Henna Altaf
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Fuzzy Topology ◽  
Real Numbers ◽  
Positive Real ◽  
Double Sequence Spaces ◽  
Intuitionistic Fuzzy ◽  
New Type

In this article we introduce the paranorm type intuitionistic fuzzy Zweier I-convergent double sequence spaces 2ZI(?,v)(p) and 2ZI 0(?,v)(p) for p = (pij) a double sequence of positive real numbers and study the fuzzy topology on these spaces.

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.

Paranorm I-convergent sequence spaces

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
Biond Tripathy ◽  
Bipan Hazarika
Keyword(s):  
Convergent Sequence ◽  
Decomposition Theorem ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Real Numbers ◽  
Positive Real ◽  
Inclusion Relations

AbstractIn this article we introduced the sequence spaces c I(p), c 0I(p), m I(p) and m 0I(p) for p = (p k), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition theorem and obtain some inclusion relations.

On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C0, C, lP, (1 ≤ P ≤ ∞), W0 and W∞

2017 ◽  
Vol 84 (3-4) ◽  
pp. 211 ◽  
Author(s):  
Bruno de Malafosse
Keyword(s):  
Sequence Spaces ◽  
Real Numbers ◽  
Positive Real ◽  
Complex Sequences

<p>Given any sequence a = (a<sub>n</sub>)<sub>n≥1</sub> of positive real numbers and any set <em>E</em> of complex sequences, we write E<sub>a</sub> for the set of all sequences y = (y<sub>n</sub>)<sub>n≥1</sub> such that y/a = (y<sub>n</sub>/a<sub>n</sub>)<sub>n≥1</sub> ∈ E; in particular, c<sub>a</sub> denotes the set of all sequences y such that y/a converges. Let Φ = {c<sub>0</sub>, c, l<sub>∞</sub>, l<sub>p</sub>, w<sub>0</sub>, w<sub>∞</sub>},(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ E<sub>a</sub>+F'<sub>x</sub> where F∈{c<sub>0,</sub>l<sub>p</sub>, w<sub>0</sub>, w<sub>∞</sub>} and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (r<sup>n</sup>)<sub>n</sub> and we deal with the case when F = F'. Finally we solve the equation E<sub>r</sub> + (l<sub>p</sub>)<sub>x</sub> = l<sub>p</sub> with E = c<sub>0</sub>, c, s<sub>1</sub>, or l<sub>p</sub> (p≥1). These results extend those stated in [10].</p>

scholarly journals On Paranorm Zweier -Convergent Sequence Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vakeel A. Khan ◽  
Khalid Ebadullah ◽  
Ayhan Esi ◽  
Nazneen Khan ◽  
Mohd Shafiq
Keyword(s):  
Convergent Sequence ◽  
Decomposition Theorem ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Real Numbers ◽  
Positive Real ◽  
Inclusion Relations

In this paper, we introduce the paranorm Zweier -convergent sequence spaces , , and , a sequence of positive real numbers. We study some topological properties, prove the decomposition theorem, and study some inclusion relations on these spaces.

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