scholarly journals On the spaces of Nörlund almost null and Nörlund almost convergent sequences

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 773-783 ◽  
Author(s):  
Orhan Tuğ ◽  
Feyzi Başar
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformations ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

In this article, the sequence spaces f0(Nt) and f (Nt) are introduced as the domain of N?rlund mean in the spaces f0 and f of almost null and almost convergent sequences which are isomorphic to the spaces f0 and f , respectively, and some inclusion relations are given. Additionally, alpha, beta and gamma duals of the sequence spaces f0(Nt) and f (Nt) are determined. Finally, the classes (?(Nt):?) and (?:?(Nt)) of matrix transformations are characterized for given sequence spaces ? and ? together with two Steinhaus type results.

scholarly journals On the Domain of the Triangle on the Spaces of Null, Convergent, and Bounded Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Naim L. Braha ◽  
Feyzi Başar
Keyword(s):  
Type Theorem ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Bounded Sequences ◽  
Convergent Sequences

We introduce the spaces of -null, -convergent, and -bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute -, -, and -duals of these spaces. Finally, we characterize some classes of matrix transformations from the spaces of -bounded and -convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.

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 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 Sequence spaces defined via Euler method and matrix transformations

2021 ◽  
Author(s):  
Pranav Sharma
Keyword(s):  
Normed Space ◽  
Lacunary Sequence ◽  
Euler Method ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Matrix Summability ◽  
Inclusion Relations ◽  
Transformation Methods

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

scholarly journals Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

2018 ◽  
Vol 36 (1) ◽  
pp. 37 ◽  
Author(s):  
Bipan Hazarika ◽  
Anupam Das
Keyword(s):  
Sequence Space ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Band Matrix ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

scholarly journals Strongly almost convergent generalized difference sequences associated with multiplier sequences

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Ayhan Esi ◽  
Binod Tripathy
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Convergent Sequences

AbstractLet Λ = (λk) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e. w 0[A,Δm,Λ,p], w 1[A,Λm,Λ,p], w ∞[A,Δm,Λ,p] and study their different properties. We also introduce ΔΛm-statistically convergent sequences and give some inclusion relations between w 1[Δm,λ,p] convergence and ΔΛm-statistical convergence.

scholarly journals Strongly Almost Lacunary -Convergent Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Adem Kılıçman ◽  
Stuti Borgohain
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Convergent Sequences

We study some new strongly almost lacunary -convergent generalized difference sequence spaces defined by an Orlicz function. We give also some inclusion relations related to these sequence spaces.

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 SOME GENERALIZED FIBONACCI DIFFERENCE SPACES DEFINED BY A SEQUENCE OF MODULUS FUNCTIONS

2017 ◽  
pp. 095 ◽  
Author(s):  
Gülsen Kılınç ◽  
Murat Candan
Keyword(s):  
Real Number ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Alpha Beta

This paper submits the sequence space $l\left( \widehat{F}\left( r,s\right),\mathcal{F},p,u\right) $ and $l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) $of non-absolute type under the domain ofthe matrix$\widehat{\text{ }F}\left( r,s\right) $ constituted by usingFibonacci sequence and non-zero real number $r$, $s$ and a sequence ofmodulus functions. We study some inclusion relations, topological andgeometric properties of these spaceses. Further, we give the $\alpha $- $%\beta $- and $\gamma $-duals of said sequence spaces and characterization ofthe classes $\left( l\left( \widehat{F}\left( r,s\right) ,\mathcal{F}%,p,u\right) ,X\right) $ and $\left( l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) ,X\right) $.

scholarly journals A survey on some paranormed sequence spaces

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1099-1122 ◽  
Author(s):  
Eberhard Malkowsky ◽  
Feyzi Başar
Keyword(s):  
Sequence Spaces ◽  
Complete List ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Comprehensive Collection ◽  
Special Cases ◽  
Bk Spaces ◽  
Convergent Sequences

This paper presents a survey of most of the known fundamental results involving the sequence spaces l(p), c0(p), c(p) and l?(p), w0(p), w(p) and w?(p), f0(p) and f (p). These spaces are generalizations of the classical BK spaces lp, c0, c and l?, the spaces wp 0, wp and wp? of sequences that are strongly summable to zero, strongly summable and strongly bounded with index p by the Ces?ro method of order 1, and of almost null and almost convergent sequences, respectively. The results inlude the basic topological properties of the generalized spaces, the complete lists of their known ?-, ?-, ?-, functional and continuous duals, and the characterizations of many classes of matrix transformations between them, in particular, the complete list of characterizations of matrix transformations between the spaces l(p), c0(p), c(p) and l?(p). Furthermore, a great number of interesting special cases are included. The presented results cover a period of four decades. They are intended to inspire the inreasing number of researchers working in related topics, and to provide them with a comprehensive collection of results they may find useful for their work.

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