Copyright © 2009 Hamdullah Şevli and Ekrem Savaş. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Denote by 𝒜k the sequence space defined by 𝒜k={(sn):∑n=1∞nk−1|an|k<∞,an=sn−sn−1} for k≥1. In a recent paper by E. Savaş and H. Şevli (2007), they proved every Cesàro matrix of order α, for α>−1, (C,α)∈B(𝒜k) for k≥1. In this paper, we consider a further extension of absolute Cesàro summability.