scholarly journals Some Properties of the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Kuldip Raj ◽  
Sunil K. Sharma
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Topological Properties ◽  
Inclusion Relations

We introduce the sequence space defined by a Musielak-Orlicz function . We also study some topological properties and prove some inclusion relations involving this space.

Generalized difference sequence space defined by |$$ \bar N $$, p k| summability and an Orlicz function in seminormed space

2010 ◽  
Vol 60 (2) ◽  
Author(s):  
Vinod Bhardwaj ◽  
Indu Bala
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
Seminormed Space ◽  
Complex Linear ◽  
Appl Math

AbstractThe object of this paper is to introduce a new difference sequence space which arise from the notions of |$$ \bar N $$, p k| summability and an Orlicz function in seminormed complex linear space. Various algebraic and topological properties and certain inclusion relations involving this space have been discussed. This study generalizes results: [ALTIN, Y.—ET, M.—TRIPATHY, B. C.: The sequence space |$$ \bar N_p $$|(M, r, q, s) on seminormed spaces, Appl. Math. Comput. 154 (2004), 423–430], [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$$ \bar N $$, p n| summability, Demonstratio Math. 32 (1999), 539–546] and [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$$ \bar N $$, p n| summability and an Orlicz function, Indian J. Pure Appl. Math. 31 (2000), 319–325].

Generalized difference sequence spaces on seminormed space defined by Orlicz functions

2008 ◽  
Vol 58 (3) ◽  
Author(s):  
Binod Tripathy ◽  
Yavuz Altin ◽  
Mikail Et
Keyword(s):  
Linear Space ◽  
Sequence Space ◽  
Orlicz Function ◽  
Difference Sequence ◽  
Topological Properties ◽  
Orlicz Functions ◽  
Inclusion Relations ◽  
Seminormed Space ◽  
Complex Linear ◽  
Difference Sequence Spaces

AbstractIn this paper we define the sequence space ℓM (Δm, p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving ℓM (Δm, p, q, s).

scholarly journals On Some Classes of Double Difference Sequences of Interval Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Kuldip Raj ◽  
Abdullah Alotaibi
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Double Difference ◽  
Difference Sequence ◽  
Topological Properties ◽  
Interval Numbers ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Interval Valued ◽  
Difference Sequence Spaces

The aim of this paper is to introduce some interval valued double difference sequence spaces by means of Musielak-Orlicz functionM=(Mij). We also determine some topological properties and inclusion relations between these double difference sequence spaces.

scholarly journals On some new modular sequence spaces

2013 ◽  
Vol 31 (2) ◽  
pp. 55 ◽  
Author(s):  
Cigdem Asma Bektas ◽  
Gülcan Atıci
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Orlicz Sequence Space ◽  
Orlicz Functions ◽  
Orlicz Sequence Spaces

Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space ℓM which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of ℓ (M), which is an AK-space, is the space h (M) . We define the sequence spaces ℓM (m) and ℓ N(m), where M = (Mk) and N = (Nk) are sequences of Orlicz functions such that Mk and Nk be mutually  complementary for each k. We also examine some topological properties of these spaces. We give the α−, β− and γ− duals of the sequence space h (M) and α− duals of the squence spaces ℓ (M, λ) and ℓ (N, λ).

scholarly journals New Difference Sequence Spaces Defined by Musielak-Orlicz Function

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
S. A. Mohiuddine ◽  
A. Kılıçman
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce new sequence spaces by using Musielak-Orlicz function and a generalizedB∧ μ-difference operator onn-normed space. Some topological properties and inclusion relations are also examined.

scholarly journals The Hahn Sequence Space Defined by the Cesáro Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Murat Kirişci
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Matrix Transformations ◽  
Space Theory ◽  
Topological Properties ◽  
Cesàro Mean ◽  
First Order ◽  
Inclusion Relations ◽  
The Matrix ◽  
Cesaro Mean

The -space of all sequences is given as such that converges and is a null sequence which is called the Hahn sequence space and is denoted by . Hahn (1922) defined the space and gave some general properties. G. Goes and S. Goes (1970) studied the functional analytic properties of this space. The study of Hahn sequence space was initiated by Chandrasekhara Rao (1990) with certain specific purpose in the Banach space theory. In this paper, the matrix domain of the Hahn sequence space determined by the Cesáro mean first order, denoted by , is obtained, and some inclusion relations and some topological properties of this space are investigated. Also dual spaces of this space are computed and, matrix transformations are characterized.

scholarly journals Generalized Differenceλ-Sequence Spaces Defined by Ideal Convergence and the Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Awad A. Bakery
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
The Ideal

We introduced the ideal convergence of generalized difference sequence spaces combining an infinite matrix of complex numbers with respect toλ-sequences and the Musielak-Orlicz function overn-normed spaces. We also studied some topological properties and inclusion relations between these spaces.

scholarly journals Sequence Spaces Defined by Musielak-Orlicz Function over -Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
A. Kılıçman
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Normed Spaces ◽  
Inclusion Relations

In the present paper we introduce some sequence spaces overn-normed spaces defined by a Musielak-Orlicz function . We also study some topological properties and prove some inclusion relations between these spaces.

scholarly journals NEW GENERALIZED CIESARO SPACE WITH SOME TOPOLOGICAL PROPERTIES

2021 ◽  
pp. 253-262
Author(s):  
Rayees Ahmad
Keyword(s):  
Sequence Space ◽  
Subject Classification ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Space

The sequence space introduced by M. Et and have studied its various properties. The aim of the present paper is to introduce the new pranormed generalized difference sequence space. and , We give some topological properties and inclusion relations on these spaces. 2010 AMS Mathematical Subject Classification: 46A45; 40C05.

scholarly journals Some Paranormed Double Difference Sequence Spaces for Orlicz Functions and Bounded-Regular Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Kuldip Raj ◽  
Abdullah Alotaibi
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Double Difference ◽  
Difference Sequence ◽  
Topological Properties ◽  
Orlicz Functions ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

The aim of this paper is to introduce some new double difference sequence spaces with the help of the Musielak-Orlicz functionℱ=(Fjk)and four-dimensional bounded-regular (shortly,RH-regular) matricesA=(anmjk). We also make an effort to study some topological properties and inclusion relations between these double difference sequence spaces.

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