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

In this paper a general theorem concerning the | 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 ∑ a n λ n to be summable | A , δ | k , k ≧ 1 , 0 ≦ δ < 1 / k , by using quasi-power-increasing sequences.