Abstract. We extend known Tauberian results concerning the power series method of summability to results concerning the more general summability method $D_{\lambda,a}$ based on the Dirichlet series $\sum a_n e^{- \lambda_nx}.$

AMS Subject Classification (1991): 40G10, 40E05

Keyword(s): Tauberian, Dirichlet series methods

Received November 11, 1998 and in revised form December 21, 1998. (Registered under 2678/2009.)