Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) - Min Zhang (Abstract and Applied Analysis)
This work deals with Feigenbaum’s functional equation f(φ(x))=φp(f(x)), φ(0)=1, 0≤φ(x)≤1, x∈ [0, 1], where p≥2 is an integer, φp is the p-fold iteration of φ, and f(x) is a strictly increasing continuous function on [0, 1] that satisfies f(0)=0, f(x)<x, (x∈(0, 1]). Using a constructive method, we discuss the existence of non-single-valley continuous solutions of the above equation.