NECESSARY AND SUFFICIENT TAUBERIAN CONDITIONS UNDER WHICH CONVERGENCE FOLLOWS FROM SUMMABILITY


Kambak C., Canak İ.

PROBLEMY ANALIZA-ISSUES OF ANALYSIS, vol.10, no.2, pp.44-53, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.15393/j3.art.2021.10110
  • Title of Journal : PROBLEMY ANALIZA-ISSUES OF ANALYSIS
  • Page Numbers: pp.44-53
  • Keywords: summability by A(r,p) method, slow oscillation, slow decrease, Tauberian condition

Abstract

In this paper, we introduce the summability method A(r,p) and obtain necessary and sufficient Tauberian conditions under which the ordinary convergence of a sequence follows from its summability A(r,p). The main results are new Tauberian theorems for the summability method A(r,p), which are generalizations of the corresponding Tauberian theorems for the summability method A(r) introduced by Basar.