Some extended Tauberian theorems for (A)(k) (C, α) summability method

İbrahim Çanak

doi:10.4025/actascitechnol.v36i4.16605

Abstract

In this paper, some new Tauberian conditions are introduced for ( A ) ( k ) ( C , α ) summability method.

Highlights

Let an be a given infinite series of real numbers with the sequence of n-th partial sums =
Our aim in this paper is to introduce some new conditions in terms of
Some new Tauberian conditions in terms of (C, ) mean of ( n ) have been obtained to recover (C, ) convergence of ( n ) and slow oscillation of (C, ) mean from ( A)(k) (C, ) summability of ( n )

Summary

Introduction

Some new Tauberian conditions are introduced for ( A)(k ) (C , ) summability method. A sequence (sn ) is said to be (C, ) summable to s and we write sn s (C, ) , if A generalization of Abel summability is introduced by (LITTLEWOOD, 1967) as follows.

Results

Conclusion