Some Tauberian theorems for regularly generated sequences

In this paper, we establish some Tauberian theorems for the Abel summability method in terms of regularly generated sequences which generalizes some results obtained in Çanak and Totur [İ. Çanak, Ü. Totur, A note on Tauberian theorems for regularly generated sequences, Tamkang J. Math. 39 (2) (2008) 187–191].