This work deals with Feigenbaum’s functional equation ⎧ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-2-6,
author = {Min Zhang and Jianguo Si},
title = {Solutions for the p-order Feigenbaum's functional equation $h(g(x)) = g^{p}(h(x))$
},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {183-195},
zbl = {1303.39013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-2-6}
}
Min Zhang; Jianguo Si. Solutions for the p-order Feigenbaum’s functional equation $h(g(x)) = g^{p}(h(x))$
. Annales Polonici Mathematici, Tome 111 (2014) pp. 183-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-2-6/