Summability of Double Sequences and Double Series Over Non-Archimedean Fields: A Survey

DOI10.1007/978-3-030-15242-0_18zbMath1450.40005OpenAlexW2969364600MaRDI QIDQ5110843

P. N. Natarajan, Hemen Dutta

Publication date: 25 May 2020

Published in: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-15242-0_18

zbMATH Keywords

double seriesTauberian theoremdouble sequencePringsheim convergenceregular matrixSchur's theoremnon-Archimedean fieldSteinhaus theoremweighted mean methodNörlund methodconservative matrixSilverman-Toeplitz theoremNatarajan method\((M, \lambda_m, n)\) method4-dimensional infinite matrix

Mathematics Subject Classification ID

Cesàro, Euler, Nörlund and Hausdorff methods (40G05) Multiple sequences and series (40B05) Tauberian theorems (40E05) Non-Archimedean analysis (26E30) Research exposition (monographs, survey articles) pertaining to sequences, series, summability (40-02)

Cites Work

• Silvermann-Toeplitz theorem for double sequences and series and its application to Nőrlund means in non-Archimedean fields
• On conservative matrix methods for double sequence spaces
• Product theorems for certain summability methods in non-Archimedean fields
• An introduction to ultrametric summability theory
• Convergence Methods for Double Sequences and Applications
• On the Pringsheim convergence of double series
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