Okay, here's the question:
Suppose we want to find a solution to $\frac{1} {2} e^{x} - x = 0 $ on the interval [0,1]. Show how to restate this problem as a fixed point problem.
This is the first part of the question, but I think I'll know how to do the second part once I know this. I think I get what is being asked.. We need to find a suitable g(x) that converges. But I can't find a dumbed down version in my notes of the process for this but I know you use MVT or the Contraction Mapping Theorem. It's an exam type question that comes up commonly so if someone could simplify this method or even just show me by example that would be great! :) Thanks in advance!