On a scale of Abel-type summability methods

Abstract

1. Introduction. In this note Abel-type summability methods (Aλ) are defined and some of their properties investigated.Letand let {sn} be any sequence of numbers. Ifis convergent for all x in the open interval (0,1) and tends to a finite limit s as x → 1 in (0,1), we shall say that the sequence is Aλ-convergent to s and write sn → s (Aλ;). The A0 method is the ordinary Abel method.