Some inclusion theorems

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 Z-spaces

1. N o t a t i o n a n d pre l iminary ideas . A sequence space is a vector subspace of the space co of all real (or complex) sequences. A sequence space E with a locally convex topology r is called a Kspace if the inclusion map E —* co is continuous, when co is endowed with the product topology (co = II^Li (R)*). A i£-space E with a Frechet (i.e., complete, metrizable and locally convex) topol...

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.

Some Useful Network Theorems

Thévenin’s theorem is used to represent a part of a network by a voltage source Vt and a series impedance Zt , as shown in Fig. D.1. Figure D.1(a) shows a network divided into two parts, A and B. In Fig. D.1(b), part A of the network has been replaced by its Thévenin equivalent: a voltage source Vt and a series impedance Zt . Figure D.1(c) illustrates how Vt is to be determined: Simply open-cir...

Some Theorems on Coverings