A Tauberian theorem for (A)(C,α)(A)(C,α) summability

In this paper we prove a Tauberian theorem for (A)(C,α)(A)(C,α) summability method, which extends the well-known classical Tauberian theorem due to Tauber [A. Tauber, Ein satz der Theorie der unendlichen Reihen, Monatsh. f. Math. 8 (1897) 273–277].