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).

On the space of p -summable difference sequences of order m , (1 ≦ p < ∞)

2006 ◽  
Vol 43 (4) ◽  
pp. 387-402 ◽  
Author(s):  
Bilâl Altay
Keyword(s):  
Sequence Space ◽  
Difference Sequence ◽  
Order Difference ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
The Matrix ◽  
The Difference ◽  
Matrix Mappings ◽  
Difference Sequence Spaces

The difference sequence spaces ℓ ∞ (Δ), c (Δ) and c0 (Δ) were studied by  Kizmaz [8]. The difference sequence space bvp , generated from the space ℓ p , has recently been introduced by Başar and Altay [5]. Several papers deal with the sets of sequences whose mth order difference are bounded, convergent or convergent to zero. The main purpose of the present paper is to introduce the space ℓ p (Δ (m) ) consisting of all sequences whose mth order differences are p -absolutely summable, and is to fill up the gap in the existing literature. Moreover, we give some topological properties and inclusion relations, a Schauder basis and determine the α-, β-, γ- and f- duals of the space ℓ p (Δ (m) ). The last section of the paper has been devoted to the characterization of the matrix mappings on the sequence space ℓ p (Δ (m) ).

scholarly journals On a class of fuzzy sets defined by Orlicz functions

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 789-796 ◽  
Author(s):  
Et Mikail ◽  
Mohammad Mursaleen ◽  
Mahmut Isık
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Difference Operator ◽  
Orlicz Function ◽  
Complex Numbers ◽  
Orlicz Functions ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Sequences Of Fuzzy Numbers ◽  
The Difference

The idea of difference sequences of real (or complex) numbers was generalized by Et and ?olak [9]. In this paper, using the difference operator ?m and an Orlicz function, we introduce and examine a class of sequences of fuzzy numbers. We study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to this class.

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].

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.

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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