Does anyone know how to go about finding an example of a function with no periodic point and only one fixed point. This f is continuous in an interval I, and I c f(I). As an addendum, can this fixed point be repellant, given the above conditions? I believe that the answer is no, but that's going of intuition and not any rigorous proof atm
I've been using [0,1] as the interval, and I figure that I need a piece wise function that has a negative slope, but I've been at it for a bit and can't figure it out. Any help would be greatly appreciated!