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The Subspace of Almost Convergent Sequences
Siberian Mathematical Journal, 2021The paper deals with a well-known summability method, called almost convergence method. The authors investigate the subspace of almost convergence sequences. They obtain some related theorems and convergence results using sine functions.
Zvolinskii, R. E., Semenov, E. M.
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2021
Summary: The objective of this paper is to study certain properties of absolute almost convergence which was introduced by the authors and \textit{B. Kuttner} [Trans. Am. Math. Soc. 283, 729-739 (1984; Zbl 0546.46004)].
Das, G., Nanda, S.
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Summary: The objective of this paper is to study certain properties of absolute almost convergence which was introduced by the authors and \textit{B. Kuttner} [Trans. Am. Math. Soc. 283, 729-739 (1984; Zbl 0546.46004)].
Das, G., Nanda, S.
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On Almost Convergent and Statistically Convergent Subsequences
Acta Mathematica Hungarica, 2001A bounded sequence \(s=(s_{n})\) is almost convergent to \(L\) if \[ \lim_{k}\frac{1}{k}\sum_{i=0}^{n-1}s_{n+i}=L,\quad \text{uniformly in }n . \] We write \(f\)-\(\lim s=L\) and \(\mathbf F=\{s=(s_{n}): f\text{-}\lim s=L\text{ for some }L\}.\) The sequence \(s=(s_{n})\) is called statistically convergent to \(L\) provided that \(\lim_{n}n^{-1}\left ...
Miller, H. I., Orhan, C.
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A variation on absolutely almost convergence
AIP Conference Proceedings, 2018International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 25-30, 2017 -- Thessaloniki ...
Cakalli, Huseyin, Taylan, Iffet
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Acta Mathematica Hungarica, 1999
Regular convergence of multiple sequences, introduced by G.H.Hardy and F.Moricz, can be generalized to almost convergent sequences in various ways. In the paper classes of almost convergent double sequences with a kind of uniform regularity are studied. These classes are in some respects similar to the class of regular sequences.
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Regular convergence of multiple sequences, introduced by G.H.Hardy and F.Moricz, can be generalized to almost convergent sequences in various ways. In the paper classes of almost convergent double sequences with a kind of uniform regularity are studied. These classes are in some respects similar to the class of regular sequences.
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On the difference spaces of almost convergent and strongly almost convergent double sequences
Positivity, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Çapan, Hüsamettin, Başar, Feyzi
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Absolute Almost Convergence and Riesz Convergence
2014In this chapter, we define the notion of almost bounded variation and absolute almost convergence for double sequences. We use the definition of absolute almost convergence to define absolute almost conservative and absolute almost regular matrices and find necessary and sufficient conditions to characterize these matrices.
M. Mursaleen, S. A. Mohiuddine
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A generalization of almost convergence
Analysis Mathematica, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical Proceedings of the Cambridge Philosophical Society, 1979
The concept of strong almost convergence was introduced in (2), where the matrices summing every strongly almost convergent sequence, leaving the limit invariant, were characterized.
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The concept of strong almost convergence was introduced in (2), where the matrices summing every strongly almost convergent sequence, leaving the limit invariant, were characterized.
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