Limitation theorems for some methods of summability

Some inclusion theorems for absolute summability

Inclusion of absolute summability domains of matrices Factorable matrices Summability method of Cesàro a b s t r a c t In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely conve...

Inclusion Theorems for Absolute Summability Methods

In this paper we have proved two theorems concerning an inclusion between two absolute summability methods by using any absolute summability factor.

On Some Mercerian Theorems in Summability

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.

One-sided Tauberian Theorems for Dirichlet Series Methods of Summability

We extend recently established two-sided or O-Tauberian results concerning the summability method Dλ,a based on the Dirichlet series ∑ ane−λnx to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which Dλ,a-summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high in...