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.

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 the generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

Generalized Sequence Spaces in 2-Normed Spaces Defined by Ideal and a Modulus Function

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudhir Kumar ◽  
Vijay Kumar ◽  
S.S. Bhatia
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Topological Properties ◽  
Normed Spaces ◽  
New Class ◽  
Difference Sequences ◽  
Convergent Sequences

AbstractThe main objective of this paper is to define some new kind of generalized convergent sequence spaces with respect to a modulus function, and difference operator Δm, m ≥ 1 in a 2-normed space. We also examine some topological properties of the resulting sequence spaces. Finally, we have introduced a new class of generalized convergent sequences with the help of an ideal and difference sequences in the same space.

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.

scholarly journals Spaces of Ideal Convergent Sequences

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Ideal Convergence ◽  
Convergent Sequences

In the present paper, we introduce some sequence spaces using ideal convergence and Musielak-Orlicz functionℳ=Mk. We also examine some topological properties of the resulting sequence spaces.

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 Topological properties and matrix transformations of certain ordered generalized sequence spaces

1995 ◽  
Vol 18 (2) ◽  
pp. 341-356 ◽  
Author(s):  
Manjul Gupta ◽  
Kalika Kaushal
Keyword(s):  
Sequence Space ◽  
Topological Structure ◽  
Necessary Conditions ◽  
Riesz Space ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Vector Valued ◽  
Locally Convex

In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space(X,τ)and a scalar valued sequence spaceλ, on the vector valued sequence spaceλ(X)which is formed and topologized with the help ofλandX, and vice versa. Besides,we also characterizeo-matrix transformations fromc(X),ℓ∞(X)to themselves,cs(X)toc(X)and derive necessary conditions for a matrix of linear operators to transformℓ1(X)into a simple ordered vector valued sequence spaceΛ(X).

scholarly journals Lacunary sequences of complex uncertain variables defined by Orlicz functions

2021 ◽  
Vol 40 (2) ◽  
pp. 355-370
Author(s):  
Pranab Jyoti Dowari ◽  
Binod Chandra Tripathy
Keyword(s):  
Uncertainty Theory ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Uncertain Variables ◽  
Lacunary Sequences ◽  
New Class ◽  
Orlicz Functions ◽  
Inclusion Relations ◽  
Convergent Sequences

Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated.

Matrix transformations between the sequence spaces and certain BK spaces

2004 ◽  
Vol 147 (2) ◽  
pp. 377-396 ◽  
Author(s):  
Eberhard Malkowsky ◽  
Vladimir Rakočević ◽  
Snežana Živković
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformations ◽  
Bk Spaces

scholarly journals On Generalized Difference Hahn Sequence Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Kuldip Raj ◽  
Adem Kiliçman
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Inclusion Relations

We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaceshpℱ,u,Δrare investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized.

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