By considering a class of
Nörlund means that covers as a subclass the corresponding (C) means, we
obtain in the present paper, several results concerning absolute Nörlund
summability and deduce from these the corresponding |C| results as special
cases. What is indeed remarkable, is that a special case of our Theorem 2
improves an earlier result due to Bosanquet and Hyslop in dropping one of the
two independent conditions used by them. Further, the proofs of some of
our results are shorter and even more direct than the proofs given for the
corresponding special cases by using equivalent Riesz means instead of (C)
means.
