Some Tauberian Remainder Theorems for Hölder 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 Hölder 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
• Hölder summability

AMS Subject Classification:

• 40E05
• 40G05