On relations between Nörlund and Riesz means

Ikuko Kayashima

Vol. 49 (1973), No. 2, 391–396

DOI: 10.2140/pjm.1973.49.391

Abstract

Several results on relations between (absolute) Nörlund summability and (absolute) Riesz summability are known. Among them, Dikshit gives sufficient conditions for |N,q_n|⊆|N,p_n| when the sequence {p_n} is nonincreasing. The purpose of this paper is to give sufficient conditions for |N,p_n|⊆|N, q_n| or |N,q_n|⊆|N,p_n| when {p_n} 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,p_n) and (N,p_n) summability.

Mathematical Subject Classification 2000

Primary: 40D25

Secondary: 40G05

Milestones

Received: 30 August 1972

Published: 1 December 1973