A summability factor theorem for absolute summability involving -quasi-monotone and almost increasing sequences

Quite recently Bor [H. Bor, An application of almost increasing and δ -quasi-monotone sequences, JIPAM. J. Inequal. Pure Appl. Math. 1 (2) (2000). Article 18, 6 pp.] has proved a theorem on | N ¯ p n | k -summability factors of an infinite series. The present paper deals with a further generalization of his result.