Conservative inclusion of N\"orlund methods

TL;DR

This paper establishes practical conditions under which convergence relative to one Nörlund summation method implies convergence relative to another, without needing limit preservation, enhancing understanding of Nörlund methods.

Contribution

It provides necessary and sufficient conditions for the inclusion of convergence in Nörlund summation methods without the limit preservation constraint.

Findings

Identifies conditions for convergence inclusion between Nörlund methods

Eliminates the need for limit preservation in convergence comparison

Enhances practical understanding of Nörlund summation methods

Abstract

We offer practical necessary and sufficient conditions in order that every sequence convergent relative to the N\"orlund summation method $(N, p)$ be convergent relative to the N\"orlund summation method $(N, q)$ without the requirement that limits be preserved.