SOME FİXED POİNT THEOREMS IV

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 D.1(b), part A of the network has been replaced by its Thévenin equivalent: a voltage source Vt and a series impedance Zt .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

Some Fixed Point Theorems

Introduction. We wish to summarize here some new asymptotic fixed point theorems. By an asymptotic fixed point theorem we mean roughly a theorem in functional analysis in which the existence of fixed points of a map ƒ is proved with the aid of assumptions on the iterates f of ƒ. Such theorems have proved of use in the theory of ordinary and functional differential equations (see [7], [8], [9] a...

Some Structure Theorems for

Some Matching Theorems

A graph G is said to be even if its vertices can be put into two distinct classes A and B so that no two vertices of the same class are joined by an edge. If in addition each class contains exactly n representatives, G is said to be of type (n, n) . In what follows all our graphs will be of this form . Let every vertex in A be joined to every vertex in B . Then we say that G is saturated. A mat...