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.

SOME DIFFERENCE SEQUENCE SPACES GENERATED BY DE LA VALLÉE-POUSSIN MEAN

2013 ◽  
Vol 06 (02) ◽  
pp. 1350018
Author(s):  
P. D. Srivastava ◽  
Atanu Manna
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Modular Structure ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
De La Vallée Poussin ◽  
Difference Sequence Spaces

A difference sequence space using φ-function and involving the concept of de la Vallée-Poussin mean is introduced. Inclusion relations, structural and topological properties of this space are investigated. By introducing a modular structure, the equality of the countably and uniformly countably modulared spaces is obtained.

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].

On New Difference Sequence Space and Their Generalised Almost Statistical Convergence

2020 ◽  
pp. 212-219
Author(s):  
Ajaya Kumar Singh
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Convergent Sequence ◽  
Difference Sequence ◽  
Almost Convergence ◽  
Topological Properties ◽  
Statistical Limit ◽  
Difference Sequence Space ◽  
Limit Functional ◽  
Convergent Sequences

The object of the present paper is to introduce the notion of generalised almost statistical (GAS) convergence of bounded real sequences, which generalises the notion of almost convergence as well as statistical convergence of bounded real sequences. We also introduce the concept of Banach statistical limit functional and the notion of GAS convergence mainly depends on the existence of Banach statistical limit functional. We prove the existence of Banach statistical limit functional. Also, the existence GAS convergent sequence, which is neither statistical convergent nor almost convergent. Lastly, some topological properties of the space of all GAS convergent sequences are investigated.

On some new generalized difference sequence spaces on seminormed spaces defined by a sequence of Orlicz functions

2011 ◽  
Vol 61 (2) ◽  
Author(s):  
Çiğdem Bektaş
Keyword(s):  
Linear Space ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Orlicz Functions ◽  
Inclusion Relations ◽  
Complex Linear ◽  
Difference Sequence Spaces

AbstractIn this paper we define the sequence space ℓ M(Δυm, p, q, s) on a seminormed complex linear space, by using a sequence of Orlicz functions. We study some algebraic and topological properties. We prove some inclusion relations involving ℓ M(Δυm, p, q, s). spaces

On a class of difference sequences related to the ℓp space defined by Orlicz functions

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
Binod Tripathy ◽  
Sabita Mahanta
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Difference Sequence ◽  
Orlicz Functions ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
The Difference

AbstractIn this article we introduce the difference sequence space m(M, Δ, φ) using the Orlicz function. We study its different properties like solidity, completeness etc. Also we obtain some inclusion relations involving the space m(M, Δ, φ).

scholarly journals On Vector-Valued Generalized Lorentz Difference Sequence Space

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Birsen Sağır ◽  
Oğuz Oğur
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
Vector Valued ◽  
Difference Sequence Spaces

We introduce generalized Lorentz difference sequence spaces d(v,Δ,p). Also we study some topologic properties of this space and obtain some inclusion relations.

On the paranormed Nörlund difference sequence space of fractional order and geometric properties

2021 ◽  
Vol 71 (1) ◽  
pp. 155-170
Author(s):  
Taja Yaying
Keyword(s):  
Fractional Order ◽  
Sequence Space ◽  
Difference Operator ◽  
Difference Sequence ◽  
Topological Properties ◽  
Fractional Difference ◽  
Geometric Properties ◽  
Nörlund Matrix ◽  
Difference Sequence Space ◽  
New Space

Abstract In this article we introduce paranormed Nörlund difference sequence space of fractional order α, Nt (p, Δ(α)) defined by the composition of fractional difference operator Δ(α), defined by ( Δ ( α ) x ) k = ∑ i = 0 ∞ ( − 1 ) i Γ ( α + 1 ) i ! Γ ( α − i + 1 ) x k − i , $\begin{array}{} \displaystyle (\Delta^{(\alpha)}x)_k=\sum_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i}, \end{array}$ and Nörlund matrix Nt . We give some topological properties, obtain the Schauder basis and determine the α−, β− and γ-duals of the new space. We characterize certain matrix classes related to this new space. Finally we investigate certain geometric properties of the space Nt (p, Δ(α)).

DIFFERENCE SEQUENCE SPACE M(M,Ø,ÄMN,P) F OF FUZZY REAL NUMBERS

2008 ◽  
Vol 13 (4) ◽  
pp. 577-586 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Stuti Borgohain
Keyword(s):  
Sequence Space ◽  
Difference Sequence ◽  
Real Numbers ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
Fuzzy Real Numbers ◽  
The Difference

The difference sequence space m(M, ø, Äm n,p) F of fuzzy real numbers for both 1 ≤ p < 8 and 0 < p < 1, is introduced. Some properties of this sequence space like solidness, symmetricity, convergence-free are studied. Some inclusion relations involving this sequence space are obtained.

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.

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