I had my exam about a week ago, and here's one problem from it.
For which values of can we use the fixed-point iteration to solve the following equation,
I know the fixed-point iteration will converge if for all . I get,
, and so . From this I conclude that .
I now define two function, and . When , a solution exists when , that is when .
Something smells here, but I don't know what. Hints are very welcome!