scholarly journals On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 789
Author(s):  
Orhan Tuğ ◽  
Vladimir Rakočević ◽  
Eberhard Malkowsky
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Double Sequences ◽  
Real Numbers ◽  
Band Matrix ◽  
Double Sequence Spaces ◽  
Double Sequence Space ◽  
Inclusion Relations ◽  
Matrix Mappings

Let E represent any of the spaces M u , C ϑ ( ϑ = { b , b p , r } ) , and L q ( 0 < q < ∞ ) of bounded, ϑ -convergent, and q-absolutely summable double sequences, respectively, and E ˜ be the domain of the four-dimensional (4D) infinite sequential band matrix B ( r ˜ , s ˜ , t ˜ , u ˜ ) in the double sequence space E, where r ˜ = ( r m ) m = 0 ∞ , s ˜ = ( s m ) m = 0 ∞ , t ˜ = ( t n ) n = 0 ∞ , and u ˜ = ( u n ) n = 0 ∞ are given sequences of real numbers in the set c ∖ c 0 . In this paper, we investigate the double sequence spaces E ˜ . First, we determine some topological properties and prove several inclusion relations under some strict conditions. Then, we examine α -, β ( ϑ ) -, and γ -duals of E ˜ . Finally, we characterize some new classes of 4D matrix mappings related to our new double sequence spaces and conclude the paper with some significant consequences.

scholarly journals On Some I-Convergent Double Sequence Spaces of Fuzzy Real Numbers Defined by Modulus Function

2015 ◽  
Vol 55 (1) ◽  
pp. 19-28
Author(s):  
Manmohan Das
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Real Numbers ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties ◽  
Fuzzy Real Numbers

Abstract In this article our aim to introduce some new I-convergent double sequence spaces of fuzzy real numbers defined by modulus function and studies their some topological and algebraic properties. Also we establish some inclusion relations.

scholarly journals On Some Lacunary Almost Convergent Double Sequence Spaces and Banach Limits

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Metin Başarır ◽  
Şükran Konca
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Almost Convergence ◽  
Double Sequences ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Banach Limits ◽  
Sublinear Functionals

The object of this paper is to introduce some new sequence spaces related with the concept of lacunary strong almost convergence for double sequences and also to characterize these spaces through sublinear functionals that both dominate and generate Banach limits and to establish some inclusion relations.

scholarly journals Double Sequence Spaces by Means of Orlicz Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdullah Alotaibi ◽  
M. Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Orlicz Functions ◽  
Double Sequence Spaces ◽  
Inclusion Relations

We define some classes of double entire and analytic sequences by means of Orlicz functions. We study some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined.

scholarly journals Double sequence spaces defined by a sequence of modulus functions

2012 ◽  
Vol 21 (2) ◽  
pp. 203-213
Author(s):  
KULDIP RAJ ◽  
◽  
SUNIL K. SHARMA ◽  
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Double Sequence Spaces ◽  
Inclusion Relations

In the present paper we introduce double sequence spaces defined by a sequence of modulus functions F = (fk,l). We also make an effort to study some topological properties and inclusion relations between these spaces.

scholarly journals On Zweier I-convergent double sequence spaces

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3361-3369 ◽  
Author(s):  
Vakeel Khan ◽  
Nazneen Khan
Keyword(s):  
Double Sequence ◽  
Decomposition Theorem ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

In this article we introduce the Zweier I-convergent double sequence spaces 2ZI, 2ZI0 and 2ZI1. We prove the decomposition theorem and study topological properties, algebraic properties and some inclusion relations on these spaces.

Some Double Sequence Spaces Generated by Four-Dimensional Pascal Matrix

2021 ◽  
Vol 09 (08) ◽  
Author(s):  
Ahmadu Kiltho ◽  
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Topological Properties ◽  
Matrix Domain ◽  
Double Sequence Spaces ◽  
Pascal Matrix

The purpose of this paper is to discover and examine a four-dimensional Pascal matrix domain on Pascal sequence spaces. We show that they are spaces and also establish their Schauder basis, topological properties, isomorphism and some inclusions.

scholarly journals On the Characterization of Some Classes of Four-Dimensional Matrices and Almost B-Summable Double Sequences

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Matrix Classes ◽  
Related Literature ◽  
Double Sequence Spaces

We firstly summarize the related literature about Br,s,t,u-summability of double sequence spaces and almost Br,s,t,u-summable double sequence spaces. Then we characterize some new matrix classes of Ls′:Cf, BLs′:Cf, and Ls′:BCf of four-dimensional matrices in both cases of 0<s′≤1 and 1<s′<∞, and we complete this work with some significant results.

scholarly journals Some New Double-Sequence Spaces in 2-Normed Spaces Defined by Ideal Convergence and an Orlicz Function

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Orhan Tug ◽  
Mutlay Dogan ◽  
Abdullah Kurudirek
Keyword(s):  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Double Sequence Spaces ◽  
Difference Sequence Spaces

We generalize some sequence spaces from single to double, we study some topological properties of these double sequence spaces by using ideal convergence, difference sequence spaces, and an Orlicz function in 2-normed spaces, and we give some results related to these sequence spaces.

scholarly journals Some Double Sequence Spaces of Fuzzy Real Numbers of Paranormed Type

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Bipul Sarma
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Real Numbers ◽  
Double Sequence Spaces ◽  
Fuzzy Real Numbers ◽  
Sequence Algebra ◽  
Inclusion Results

We study different properties of convergent, null, and bounded double sequence spaces of fuzzy real numbers like completeness, solidness, sequence algebra, symmetricity, convergence-free, and so forth. We prove some inclusion results too.

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