General theorem for the existence of iterative roots of homeomorphisms with periodic points (Q439275)

The paper contains results concerning the equation \(G^m=F\), where \(F\) is a given continuous orientation-preserving mapping of the unit circle \(S^1\) into itself with fixed or periodic points and \(m\) is a fixed integer \(>1\). The unknown function \(G: S^1\to S^1\) is assumed to be continuous and orientation-preserving as well. These results generalize results found earlier by the author.