A summability factor theorem involving an almost increasing sequence for generalized absolute summability

In this paper we prove a general theorem on vertical bar A; 8 vertical bar(k)-summability factors of infinite series under suitable conditions by using an almost increasing sequence, where A is a lower triangular matrix with non-negative entries. Also, we deduce a similar result for the weighted mean method. (C) 2007 Elsevier Ltd. All rights reserved.