Vol. 49, No. 2, 1973

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On relations between Nörlund and Riesz means

Ikuko Kayashima

Vol. 49 (1973), No. 2, 391–396

Several results on relations between (absolute) Nörlund summability and (absolute) Riesz summability are known. Among them, Dikshit gives sufficient conditions for |N,qn||N,pn| when the sequence {pn} is nonincreasing. The purpose of this paper is to give sufficient conditions for |N,pn||N, qn| or |N,qn||N,pn| when {pn} is monotone. The results obtained here are also absolute summability analogues of Ishiguro’s theorems and Kuttner and Rhoades’ theorems which state the inclusion relations between (N,pn) and (N,pn) summability.

Mathematical Subject Classification 2000
Primary: 40D25
Secondary: 40G05
Received: 30 August 1972
Published: 1 December 1973
Ikuko Kayashima