On iterations of Darboux functions
Let \(f\) be a function from \(\mathbb{R}\) to \(\mathbb{R}\), let \(A\) be a subset of \(\mathbb{R}\), and let for any \(x\) in \(\mathbb{R}\) there be an \(n\) such that \(f^ n(x)\in A\). Under what conditions \(f\) has a fixed point in \(A\)? The author considers this problem, e.g., for weakly connected or Darboux functions. Also, some examples and open problems are given.
scientific article; zbMATH DE number 756679