Tauberian Remainder Theorems for the Weighted Mean Method of Summability

Abstract

Using the weighted general control modulo, we prove several Tauberian remainder theorems for the weighted mean method of summability. Our results generalize the results proved by Meronen and Tammeraid [Math. Model. Anal. 18 (1) 2013, 97–102].

Keywords:

• weighted general control modulo
• Tauberian remainder theorem
• weighted mean method
• λ-bounded sequence

AMS Subject Classification:

• 40C05
• 40E05
• 40G05