Abstract
Mazhar (1971) gave the characterization for the series ∑anϵn to be summable |N,pn| whenever ∑an is
summable |C,α|k, α≥0, k≥1. Here we prove two
theorems, the first concerns the sufficient conditions and the
second the necessary conditions satisfied by {ϵn} in order to have ∑anϵn summable |N¯,pn|k whenever ∑an is summable |C,α|k, k≥1.