Generalised quasi-Nörlund summability

Premalata Mohapatro

Vol. 68 (1977), No. 1, 177–195

DOI: 10.2140/pjm.1977.68.177

Abstract

Just as (N,p,q) generalises Nörlund methods, so also, in this paper we define generalised quasi-Nörlund Method (N^∗,p,q) generalising the quasi-Nörlund method due to Thorpe.

To begin with, we have determined the inverse of a generalised quasi-Nörlund matrix in a limited case. BesiBes, limitation Theorems for both ordinary and absolute (N^∗,p,q) summability have been established.

Finally we have established an Abelian Theorem (the main theorem) for (N^∗,p,q) ⇒ (J,q), where (J,q) is a power series method which reduces to the Abel method (A) for q_n = 1 (all n).

Mathematical Subject Classification 2000

Primary: 40G05

Milestones

Received: 3 May 1976

Revised: 16 July 1976

Published: 1 January 1977