General absolute summability factor theorems involving quasi-power-increasing sequences

In this paper a general theorem concerning the |A,δ|k|A,δ|k summability methods has been proved, which generalizes two results of Şevli and Leindler [H. Şevli and L. Leindler, On the absolute summability factors of infinite series involving quasi-power-increasing sequences, Computers and Mathematics with Applications 57 (2009), 702–709]. We obtain sufficient conditions for ∑anλn∑anλn to be summable |A,δ|k|A,δ|k, k≧1k≧1, 0≦δ<1/k0≦δ<1/k, by using quasi-power-increasing sequences.