Definition 1. 1(Fixed Point). A ficed point of a function g(a)is a real number P such that P=g(P) Geometrically, the fixed points of a function y=g()are the points of intersection of y=g(a)and y=0 Definition 1. 2(Fixed-point Iteration). The iteration Pn+1=g(pn )for n=0,1 is called fi.aced-point iteration
Theorem 1.1. Assume that g is a continuous function and that ipn jooo is a se- quence generated by fixed-point iteration. If limn-ooPn=P, then P is a fixed point