Mazhar (1971) gave the characterization for the series ∑ a n ϵ n to be summable | N , p n | whenever ∑ a n 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 { ϵ n } in order to have ∑ a n ϵ n summable | N ¯ , p n | k whenever ∑ a n is summable | C , α | k , k ≥ 1 .