Multidimensional Matrix Characterization of Asymptotic I2−Equivalent and Ideal for Double Sequences

2019 ◽  
Vol 40 (6) ◽  
pp. 654-669
Author(s):  
Rabia Savaş ◽  
Richard F. Patterson
Keyword(s):  
Double Sequences ◽  
Multidimensional Matrix

Multidimensional matrix characterization of equivalent double sequences

2012 ◽  
Vol 49 (2) ◽  
pp. 269-281
Author(s):  
Richard Patterson ◽  
Ekrem Savaş
Keyword(s):  
Rate Of Convergence ◽  
Double Sequence ◽  
Double Sequences ◽  
Multidimensional Matrix ◽  
Summability Matrix

In 1936 Hamilton presented a Silverman-Toeplitz type characterization of c″0 (i.e. the space of bounded double Pringsheim null sequences). In this paper we begin with the presentation of a notion of asymptotically statistical regular. Using this definition and the concept of maximum remaining difference for double sequence, we present the following Silverman-Toeplitz type characterization of double statistical rate of convergence: let A be a nonnegative c″0−c″0 summability matrix and let [x] and [y] be member of l″ such that with [x] ∈ P0, and [y] ∈ Pδ for some δ > 0 then µ(Ax) µ(Ay). In addition other implications and variations shall also be presented.

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.

Matrix characterization of oscillation for double sequences

2008 ◽  
Vol 6 (3) ◽  
pp. 488-496
Author(s):  
Richard F. Patterson ◽  
Jeff Connor ◽  
Jeannette Kline
Keyword(s):  
Double Sequences

scholarly journals Four dimensional characterization of bounded double sequences

2004 ◽  
Vol 35 (2) ◽  
pp. 129-134 ◽  
Author(s):  
Richard F. Patterson
Keyword(s):  
Bounded Sequence ◽  
Matrix Transformations ◽  
Double Sequences ◽  
Matrix Methods ◽  
Multidimensional Analog ◽  
Dimensional Matrix ◽  
Important Theorem ◽  
Summability Matrix ◽  
Regular Summability

In 1945 Brudno presented the following important theorem: If $A$ and $B$ are regular summability matrix methods such that every bounded sequence summed by $A$ is also summed by $B$, then it is summed by $B$ to the same value. R. G. Cooke suggested that a simpler proof would be desirable. Petersen presented such a proof. The goal of the paper is to present an accessible multidimensional analog of Brudno theorem for double sequences using four dimensional matrix transformations.

scholarly journals Characterization of q-Cesàro convergence for double sequences

2017 ◽  
Vol 62 (3) ◽  
pp. 367-376
Author(s):  
Emre Taş ◽  
◽  
Cihan Orhan ◽  
Keyword(s):  
Double Sequences ◽  
Cesaro Convergence
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