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 Almost Lacunary Double Sequence Spaces Defined by Orlicz Functions in 2-Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Normed Spaces ◽  
Orlicz Functions ◽  
Double Sequence Spaces ◽  
Almost Convergent Sequence

Das and Patel (1989) introduced two new sequence spaces which are called lacunary almost convergent and lacunary strongly almost convergent sequence spaces. Móricz and Rhoades (1988) defined and studied almost P-convergent double sequences spaces. Savaş and Patterson (2005) introduce the almost lacunary strong P-convergent double sequence spaces by using Orlicz functions and examined some properties of these sequences spaces. In this paper, some almost lacunary double sequences spaces are given by using 2-normed spaces.

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 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 New Sequence Spaces and Statistical Convergence Methods for Double Sequences

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Cemal Belen ◽  
Mustafa Yildirim
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Double Sequence Spaces ◽  
Lacunary Statistical Convergence

AbstractIn this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods

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 Two valued measure and some new double sequence spaces in 2-normed spaces

2011 ◽  
Vol 61 (3) ◽  
pp. 809-825 ◽  
Author(s):  
Pratulananda Das ◽  
Ekrem Savas ◽  
Santanu Bhunia
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Double Sequence Spaces

On paranorm BVσ I-convergent double sequence spaces defined by an Orlicz function

Analysis ◽  
2017 ◽  
Vol 37 (3) ◽  
Author(s):  
Vakeel A. Khan ◽  
Hira Fatima ◽  
Sameera A. A. Abdullah ◽  
Kamal M. A. S. Alshlool
Keyword(s):  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequence Spaces

AbstractThe space

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