In this paper we have proved a theorem on generalized Nörlund summability of infinite series, which generalizes various known results. However, our theorem is as follows.

Theorem : Let {p_n} be a positive non-increasing sequence, {e_n} is a positive non-decreasing sequence and {l_n} is a non-negative, non-increasing such that

as n®¥

n Dl_n = O(l_n )

Sp_n l_n < ¥

and then the series Sa_ne_nl_n is summable by G(N, p, l).