Almost Convergence of Double Sequences

2014 ◽  
pp. 17-39
Author(s):  
M. Mursaleen ◽  
S. A. Mohiuddine
Keyword(s):  
Almost Convergence ◽  
Double Sequences

scholarly journals Generalized Almost Convergence and Core Theorems of Double Sequences

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Abdullah Alotaibi
Keyword(s):  
Banach Space ◽  
Almost Convergence ◽  
Double Sequences ◽  
Tauberian Condition ◽  
Core Equivalence

The idea of[λ, μ]-almost convergence (briefly,F[λ, μ]-convergence) has been recently introduced and studied by Mohiuddine and Alotaibi (2014). In this paper first we define a norm onF[λ, μ]such that it is a Banach space and then we define and characterize those four-dimensional matrices which transformF[λ, μ]-convergence of double sequencesx=(xjk)intoF[λ, μ]-convergence. We also define aF[λ, μ]-core ofx=(xjk)and determine a Tauberian condition for core inclusions and core equivalence.

Almost convergence of double sequences and strong regularity of summability matrices

1988 ◽  
Vol 104 (2) ◽  
pp. 283-294 ◽  
Author(s):  
F. Móricz ◽  
B. E. Rhoades
Keyword(s):  
Double Sequence ◽  
Almost Convergence ◽  
Strong Regularity ◽  
Double Sequences ◽  
Real Numbers ◽  
Average Value ◽  
Summability Matrices ◽  
Image Position

A double sequence x = {xjk: j, k = 0, 1, …} of real numbers is called almost convergent to a limit s ifthat is, the average value of {xjk} taken over any rectangle {(j, k): m ≤ j ≤ m + p − 1, n ≤ k ≤ n + q − 1} tends to s as both p and q tend to ∞, and this convergence is uniform in m and n. The notion of almost convergence for single sequences was introduced by Lorentz [1].

scholarly journals On the almost convergence of double sequences

2016 ◽  
Vol 51 (1) ◽  
pp. 175-196
Author(s):  
Davor Butković ◽  
Keyword(s):  
Almost Convergence ◽  
Double Sequences

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 Almost Conservative Four-Dimensional Matrices through de la Vallée-Poussin Mean

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Abdullah Alotaibi
Keyword(s):  
Double Sequence ◽  
Double Series ◽  
Almost Convergence ◽  
Double Sequences ◽  
Infinite Matrices ◽  
De La Vallée Poussin

The purpose of this paper is to generalize the concept of almost convergence for double sequence through the notion of de la Vallée-Poussin mean for double sequences. We also define and characterize the generalized regularly almost conservative and almost coercive four-dimensional matrices. Further, we characterize the infinite matrices which transform the sequence belonging to the space of absolutely convergent double series into the space of generalized almost convergence.

scholarly journals Almost convergence of double subsequences

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 87-93 ◽  
Author(s):  
Fikret Cunjalo
Keyword(s):  
Lebesgue Measure ◽  
Almost Convergence ◽  
Double Sequences ◽  
Second Category

Almost-convergence of double sequences (subsequences) is equivalent to almost Cauchy condition. If the set of all almost convergent subsequences of a sequence S = Snm is of the second category, then S is convergent in the simple sense. For the sequence S = Snm which almost converges to L, Lebesgue measure of the set of all its subsequences which almost converge to L is either 1 or 0. .

scholarly journals Almost convergence of complex uncertain double sequences

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 61-78
Author(s):  
Birojit Das ◽  
Binod Tripathy ◽  
Piyali Debnath ◽  
Baby Bhattacharya
Keyword(s):  
Cauchy Sequence ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Uncertain Variable ◽  
Almost Convergence ◽  
Double Sequences ◽  
Uncertain Environment ◽  
Complex Sequences ◽  
Measure Distribution

Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment. In this treatise, we extend the study of almost convergence by introducing double sequences of complex uncertain variable. Almost convergence with respect to almost surely, mean, measure, distribution and uniformly almost surely are presented and interrelationships among them are studied and depicted in the form of a diagram. We also define almost Cauchy sequence in the same format and establish some results. Conventionally we have, every convergent sequence is a Cauchy sequence and the converse case is not true in general. But taking complex uncertain variable in a double sequence, we find that a complex uncertain double sequence is a almost Cauchy sequence if and only if it is almost convergent. Some suitable examples and counter examples are properly placed to make the paper self sufficient.

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