Inclusion and equivalence relations between absolute Nörlund and absolute weighted mean summability methods

Abstract

In this paper, a set of conditions under which the absolute Nörlund summability method include in the absolute weighted mean method have been established. Three non-trivial examples to show that this inclusion holds have been given, and other three examples to show that even if both and  are regular, the inclusion fails to holds have been constructed. The paper give two non-trivial examples to show that the equivalence of these two methods may holds. Finally, we give two examples to show that inclusion may holds in only one way without the other.