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

Abstract

Inclusion, convexity and Tauberian theorems are proved for certain generalized Norlund 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 Norlund summmability methods and power series methods applied to ordinary sequences (sn) to summability of double sequences (smn) in the sense of bounded Pringsheim convergence. As examples some special methods like Cesaro methods and extensions as generalized Cesaro methods and quasi Cesaro methods are considered (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)