Solutions for the p-order Feigenbaum's functional equation $h(g(x)) = g^{p}(h(x))$

• Autorzy: Min Zhang , Jianguo Si
• Języki publikacji: EN

Abstrakty

EN

This work deals with Feigenbaum's functional equation
⎧ $h(g(x)) = g^p(h(x))$,
⎨
⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1]
where p ≥ 2 is an integer, $g^p$ is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.

Kategorie tematyczne

• 39B12: Iteration theory, iterative and composite equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 111
• Numer: 2
• Strony: 183-195

Daty

wydano

2014

Twórcy

autor

Min Zhang

• School of Science, China University of Petroleum, 266555 Qingdao, Shandong, People's Republic of China

autor

Jianguo Si

• School of Mathematics, Shandong University, 250100 Jinan, Shandong, People's Republic of China

Identyfikatory

DOI

10.4064/ap111-2-6