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

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