ABSTRACT

Suppose we are given a metric space (V,d), on which is defined an operator T. The fixed point equation is simply V =TV , and is the common form of many important mathematical problems. The Banach fixed point theorem (Theorem 6.4) applies to complete metric spaces, and defines sufficient conditions under which is can be stated that

1 A solution to V =TV exists, 2 The solution to V =TV is unique, 3 The solution to V is the limit in the given metric of the sequence Tkv0 for any

v0 ∈V.