On Absolute Cesàro Summability

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.