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A family of generalized Nörlund methods and related power series methods applied to double sequences

✍ Scribed by Ulrich Stadtmüller; Anne Tali

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
196 KB
Volume
282
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Inclusion, convexity and Tauberian theorems are proved for certain generalized Nörlund methods and power series methods applied to double sequences. Families of summability methods are developed which form a hierarchy of methods and can be used to connect matrix and power series methods. This extends various results proved in the papers [15], [9], [17] and [14] for generalized Nörlund summmability methods and power series methods applied to ordinary sequences (s~n~) to summability of double sequences (s~mn~) in the sense of bounded Pringsheim convergence. As examples some special methods like Cesàro methods and extensions as generalized Cesàro methods and quasi Cesàro methods are considered (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

On Certain Families of Generalized Nörlu
On Certain Families of Generalized Nörlund Methods and Power Series Methods
✍ U. Stadtmüller; A. Tali 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 165 KB

We consider families A of summability methods which have similar features ␣ Ž . in their construction as the family of Cesaro methods C, ␣ . Abel-type power series methods will be added to those families and inclusion and Tauberian theorems will be proved. The Tauberian and inclusion theorems proved