Tauberian theorems for power series methods applied to double sequences

DOI10.1006/jmaa.1997.5473zbMath0883.40002OpenAlexW1996102981MaRDI QIDQ1364768

Ulrich Stadtmüller, Simson Baron

Publication date: 11 March 1998

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

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5473

zbMATH Keywords

convergencepower seriessummabilityweighted meandouble sequenceTauberian conditionspower series mean

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Convergence and divergence of series and sequences of functions (40A30) Special methods of summability (40G99) Tauberian theorems (40E05)

Related Items (16)

Approximation by modified q-Gamma type operators via A-statistical convergence and power series method ⋮ Unnamed Item ⋮ Tauberian conditions under which the original convergence of double sequences follows from the statistical convergence of their weighted means ⋮ On the weighted generator of double sequences and its Tauberian conditions ⋮ Approximation via statistical convergence in the sense of power series method of Bögel-type continuous functions ⋮ Some Tauberian theorems for the weighted mean method of summability of double sequences ⋮ Approximation via statistical measurable convergence with respect to power series for double sequences ⋮ Korovkin theory via \(P_p\)-statistical relative modular convergence for double sequences ⋮ Approximation via power series method in two-dimensional weighted spaces ⋮ Tauberian theorems for weighted means of double sequences ⋮ A Korovkin-type theorem for double sequences of positive linear operators via power series method ⋮ A family of generalized Nörlund methods and related power series methods applied to double sequences ⋮ Abstract Korovkin theory for double sequences via power series method in modular spaces ⋮ Approximation of continuous periodic functions of two variables via power series methods of summability ⋮ Tauberian theorems for \((\overline{N},p,q)\) summable double sequences of fuzzy numbers ⋮ Complementary spaces and multipliers of double Fourier series for functions of bounded variation

Cites Work

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• General Nörlund transforms and power series methods
• Product theorems for summability methods of double series
• Lectures on summability
• Transformations of multiple sequences
• Tauberian Theorems for General J_p -Methods and a Characterization of Dominated Variation
• O -Tauberian Theorems for J _p -Methods with Rapidly Increasing Weights
• A refined Tauberian Theorem for Laplace transforms in dimension d>1.
• Tauberian theorems for general power series methods
• Intermediate Regular and Π Variation
• An O-Tauberian theorem and a high indices theorem for power series methods of summability
• Power series methods and almost sure convergence
• Tauberian theorems for Borel-type methods of summability

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