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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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Periodica Mathematica Hungarica, 1993
A net \((f_ n)\) of functions on a topological space \(X\) to a uniform space \((Y,{\mathcal U})\) converges almost uniformly to a function \(f\) at \(x_ 0\in X\) if for each \(U\in{\mathcal U}\) there exists a neighborhood \(W\) of \(x_ 0\) such that eventually \((f_ n(x),f(x))\in U\) for each \(x\in W\).
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A net \((f_ n)\) of functions on a topological space \(X\) to a uniform space \((Y,{\mathcal U})\) converges almost uniformly to a function \(f\) at \(x_ 0\in X\) if for each \(U\in{\mathcal U}\) there exists a neighborhood \(W\) of \(x_ 0\) such that eventually \((f_ n(x),f(x))\in U\) for each \(x\in W\).
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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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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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A generalization of almost convergence
Analysis Mathematica, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Regularity and almost sure convergence
1995Summary: We give a sufficient condition for almost sure convergence in the sense of \textit{E. Hensz} and \textit{R. Jajte} [Math. Z. 193, 413-429 (1986; Zbl 0613.46056)] to be equivalent to almost uniform convergence.
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