Some Properties of the Continuous Single-Valley Expansion Solution to the Feigenbaum’s Functional Equation

In this paper, some fundamental properties of the continuous single-valley expansion solution to Feigenbaum’s functional equation were obtained. For λe (0,1) and p ≥ 2, we will discuss the completeness of the function space which consists of unique continuous single-valley expansion solution (resp. unique continuous non-single-valley expansion solution) to p-order Feigenbaum’s functional equation. Let p,q ≥ 2. It was proved that the system of equations