scholarly journals On Zweier generalized difference ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function

2017 ◽  
Vol 35 (2) ◽  
pp. 19 ◽  
Author(s):  
Bipan Hazarika ◽  
Karan Tamanag
Keyword(s):  
Orlicz Function ◽  
Convergent Sequence ◽  
Locally Convex Space ◽  
Sequence Spaces ◽  
Infinite Matrix ◽  
Difference Matrix ◽  
New Class ◽  
Algebraic Properties ◽  
Locally Convex ◽  
Convergent Sequences

Let $\mathbf{M}=(M_k)$ be a Musielak-Orlicz function. In this article, we introduce a new class of ideal convergent sequence spaces defined by Musielak-Orlicz function, using an infinite matrix, and a generalized difference matrix operator $B_{(i)}^{p}$ in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We obtainsome relations related to these sequence spaces.

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.

Almost strongly Orlicz double sequence spaces of regular matrices and their applications to statistical convergence

2018 ◽  
Vol 11 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Kuldip Raj ◽  
Anu Choudhary ◽  
Charu Sharma
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Regular Matrix ◽  
Normed Spaces ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over [Formula: see text]-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over [Formula: see text]-normed spaces.

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.

scholarly journals On Locally Convex Topological Vector Space Valued Null Function Space c0 Defined by Semi Norm and Orlicz Function

2015 ◽  
Vol 19 (1) ◽  
pp. 62-68
Author(s):  
Narayan Prasad Pahari
Keyword(s):  
Vector Space ◽  
Function Space ◽  
Topological Vector Space ◽  
Convex Space ◽  
Orlicz Function ◽  
Locally Convex Space ◽  
New Class ◽  
And Function ◽  
Locally Convex ◽  
Class Of Functions

The aim of this paper is to introduce and study a new class c0 (S, T, Phi, Xi, u) of locally convex space T- valued functions using Orlicz function Phi as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the structures of the class c0 (S, T, Phi, Xi, u), our primarily interest is to explore some of the containment relations of the class c0 (S, T, Phi, Xi, u) in terms of different Xi and u so that such a class of functions is contained in or equal to another class of similar nature.Journal of Institute of Science and Technology, 2014, 19(1): 62-68

scholarly journals On Locally Convex Topological Vector Space Valued Paranormed Function Space Defined by Orlicz Function

2014 ◽  
Vol 14 (2) ◽  
pp. 109-116
Author(s):  
NP Pahari
Keyword(s):  
Vector Space ◽  
Function Space ◽  
Convex Space ◽  
Orlicz Function ◽  
Locally Convex Space ◽  
Similar Nature ◽  
New Class ◽  
And Function ◽  
Locally Convex ◽  
Class Of Functions

The aim of this paper is to introduce and study a new class (l∞ (X, Y, Φ, ξ, w , L), HU) of locally convex space Y- valued functions using Orlicz function Φ as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the linear topological structures of the class (l∞ (X, Y, Φ, ξ, w , L), HU) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class l∞ (X, Y, Φ, ξ, w) in terms of different ξ and w so that such a class of functions is contained in or equal to another class of similar nature. DOI: http://dx.doi.org/10.3126/njst.v14i2.10423   Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 109-116

scholarly journals Applications of Lacunary Sequences to Develop Fuzzy Sequence Spaces for Ideal Convergence and Orlicz Function

2020 ◽  
Vol 13 (5) ◽  
pp. 1131-1148
Author(s):  
Kuldip Raj ◽  
S. A. Mohiuddine
Keyword(s):  
Maximal Ideal ◽  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Infinite Matrix ◽  
Ideal Convergence ◽  
Lacunary Sequences ◽  
Algebraic Properties

In the present paper, we introduce and study ideal convergence of some fuzzy sequence spaces via lacunary sequence, infinite matrix and Orlicz function. We study some topological and algebraic properties of these spaces. We also make an effort to show that these spaces are normal as well as monotone. Further, it is very interesting to show that if $I$ is not maximal ideal then these spaces are not symmetric.

scholarly journals On Paranormed Ideal Convergent Generalized Difference Strongly Summable Sequence Spaces Defined over n-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Bipan Hazarika
Keyword(s):  
Difference Operator ◽  
Orlicz Function ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Topological Structures ◽  
New Class ◽  
Summable Sequence

We introduce a new class of ideal convergent (shortly I-convergent) sequence spaces using an Orlicz function and difference operator of order defined over the n-normed spaces. We investigate these spaces for some linear topological structures. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces. We also give some relations related to these sequence spaces.

Some criteria for nuclearity

1986 ◽  
Vol 100 (1) ◽  
pp. 151-159 ◽  
Author(s):  
M. A. Sofi
Keyword(s):  
Sequence Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Sequence Spaces ◽  
Bilinear Forms ◽  
Simple Formulation ◽  
Normal Topology ◽  
Nuclear Spaces ◽  
Locally Convex

For a given locally convex space, it is always of interest to find conditions for its nuclearity. Well known results of this kind – by now already familiar – involve the use of tensor products, diametral dimension, bilinear forms, generalized sequence spaces and a host of other devices for the characterization of nuclear spaces (see [9]). However, it turns out, these nuclearity criteria are amenable to a particularly simple formulation in the setting of certain sequence spaces; an elegant example is provided by the so-called Grothendieck–Pietsch (GP, for short) criterion for nuclearity of a sequence space (in its normal topology) in terms of the summability of certain numerical sequences.

scholarly journals Some Results on Strongly Cesáro Ideal Convergent Sequence Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Mohammad Faisal Khan
Keyword(s):  
Convergent Sequence ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

Some algebraic properties of Cesáro ideal convergent sequence spaces, C I and C 0 I , are studied in this article and some inclusion relations on these spaces are established.

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