An equivalent reformulation of summability by weighted mean methods, revisited

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 ...

Some Theorems on Weighted Mean Summability

In this paper we have proved some theorems on weighted mean summability method by using analytical and summability techniques, which also extends the well known result of Hardy on the Cesàro summability.

Local property of absolute weighted mean summability of Fourier series

We improve and generalize a result on a local property of |T |k summability of factored Fourier series due to Sarıgöl [6].

On Relations between Weighted Mean and Power Series Methods of Summability

Matrix Transformations from Absolutely Convergent Series to Convergent Sequences as General Weighted Mean Summability Methods

We prove the necessary and sufficient conditions for an infinity matrix to be a mapping, from absolutely convergent series to convergent sequences, which is treated as general weighted mean summability methods. The results include a classical result by Hardy and another by Moricz and Rhoades as particular cases.