On vertical bar A vertical bar(k) summability factors of infinite series

In an earlier paper (Rhoades, B. E. and Savas, E. Some necessary conditions for absolute matrix summability factors. Indian J. Pure Appl. Math., 2002, 33(7), 1003-1009) the authors obtained necessary conditions for the series Sigma a(n) to be absolutely summable of order k by a triangular matrix. In this paper we present sufficient conditions for absolute matrix summability factors. As a corollary we obtain a result of N. Singh (On vertical bar(N) over bar, p(n)vertical bar summability factors of infinite series. Indian J. Math., 1968, 10, 19-24).