General Tauberian conditions for weighted mean methods of summability

Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense

After a brief summary of Tauberian conditions for ordinary sequences of numbers, we consider summability of double sequences of real or complex numbers by weighted meanmethods which are not necessarily products of related weighted mean methods in one variable. Our goal is to obtain Tauberian conditions under which convergence of a double sequence follows from its summability, where convergence ...

One-sided Tauberian conditions for a general summability method

Let (un) be a sequence of real numbers and L be an additive summability method with some property. We show that if slow decrease of (un) or one-sided boundedness of the classical control modulo of the oscillatory behavior of (un) is a Tauberian condition for a general summability method L, then one-sided boundedness by a sequence with certain conditions of the general control modulo of the osci...

On Some Tauberian Conditions for Abel Summability

In this paper we introduce new Tauberian conditions for Abel summability method that include Hardy Littlewood Tauberian condition [4] as a special case. Mathematics Subject Classification: 40E05

Tauberian Theorems by Weighted Summability Method

A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers

Let X and Y be two sequence spaces and A = (ank) be an infinite matrix. If for each x ∈ X the series An(x) = ∑∞ k=0 ankxk converges for each n and the sequence Ax = (Anx) ∈ Y we say that the matrix A maps X into Y . By (X,Y ) we denote the set of all matrices which map X into Y . Let c be the set of all convergent sequences. A matrix A is called regular if A ∈ (c, c) and limn→∞Anx = limk→∞ xk f...