Tauberian conditions under which the original convergence of double sequences follows from the statistical convergence of their weighted means

DOI10.1016/j.jmaa.2006.11.017zbMath1160.40004OpenAlexW2002967249MaRDI QIDQ884368

Chi-Tung Chang, Chang-Pao Chen

Publication date: 6 June 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.11.017

zbMATH Keywords

statistical convergenceTauberian theoremsdouble sequencesslow oscillation conditions

Mathematics Subject Classification ID

Multiple sequences and series (40B05) Special methods of summability (40G99) Tauberian theorems (40E05)

Related Items (11)

Some Tauberian theorems for statistical \((C, 1)\) summability ⋮ Some Tauberian conditions on logarithmic density ⋮ Modularly weighted four dimensional matrix summability with application to Korovkin type approximation theorem ⋮ On relative weighted summability in modular function spaces and associated approximation theorems ⋮ On \(M_{\lambda_{m,n}}\)-statistical convergence ⋮ Weighted Statistical Relative Invariant Mean in Modular Function Spaces with Related approximation Results ⋮ A Tauberian theorem for ideal statistical convergence ⋮ Statistical Summability of Double Sequences by the Weighted Mean and Associated Approximation Results ⋮ Tauberian theorems for statistically \((C, 1, 1)\) summable double sequences ⋮ Tauberian theorems for the statistical convergence and the statistical (C,1,1) summability ⋮ Tauberian theorems for ordinary convergence

Cites Work

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• Pointwise convergence of multiple trigonometric series
• Tauberian theorems for power series methods applied to double sequences
• Tauberian theorems for double sequences that are statistically summable \((C,1,1)\)
• Pointwise convergence of double trigonometric series
• Tauberian theorems in the statistical sense for the weighted means of double sequences
• Tauberian theorems for Cesàro summable double sequences
• Ordinary convergence follows from statistical summability (C,1) in the case of slowly decreasing or oscillating sequences
• Statistical extensions of some classical Tauberian theorems
• Tauberian theorems for weighted means of double sequences

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