# Fixed point : error of estimation

We want to solve $f(x)=0$ via a function of iteration $x=g(x)$ that satisfies the necessaries conditions of convergence. Determine a bound of the error which is committed in each step in function of the difference between the 2 last values of the sequence. In other words, determine $C$ such that $|x_{n+1}-x_*|\leq C |x_{n+1}-x_n|$. Where $x_*$ is the zero that we are looking for.