Some Tauberian Remainder Theorems for Holder Summability

Abstract

In this paper, we prove some Tauberian remainder theorems that generalize the results given by Meronen and Tammeraid [Math. Model. Anal., 18(1):97– 102, 2013] for Holder summability method using the notion of the general control modulo of the oscillatory behaviour of nonnegative integer order.

Keywords

• Tauberian remainder theorem
• λ-bounded series
• general control modulo
• Holder summability