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On translativity of the product of Nörlund-weighted mean summability methods. (English) Zbl 0651.40010

Denot by \((N,r)\) and \(M_ q\) the sequence-to-sequence Nörlund method of summability and the sequence-to-sequence weighted mean method, respectively. The author gives the necessary and sufficient conditions for the product of two regular methods, \((N,r)M_ q\) to be translative to the right and to the left. The author proves further that even if both \((N,r)\) and \(M_ q\) are translative, the product need not be so.
Reviewer: K.Ishiguro

MSC:

40G05 Cesàro, Euler, Nörlund and Hausdorff methods