What functions can represent the 3n+1-problem? A number of such functions have been given during the past years. In this paper, a specific one is considered which has 1, 2, 3, as critical points and 1. 5, 2. 5, 3. 5, as fixed points on the interval [1, ). Another function is presented with critical points 1, 2, 3, , and fixed point 0. 5391\! on the real line.
P. Kórus (Mon,) studied this question.