Smooth solutions for the p-order functional equation f ( φ ( x ) ) = φ p ( f ( x ) )

DOI10.22436/jnsa.010.08.34zbMath1412.39020OpenAlexW2746438049MaRDI QIDQ4632586

Min Zhang, Jie Rui

Publication date: 30 April 2019

Published in: The Journal of Nonlinear Sciences and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.22436/jnsa.010.08.34

zbMATH Keywords

functional equationconstructive methodunimodal-even-smooth solution

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12)

Cites Work

• The general exact bijective continuous solution of Feigenbaum's functional equation
• The universal metric properties of nonlinear transformations
• Fixed points of Feigenbaum's type for the equation \(f^ p(\lambda x)\equiv \lambda f(x)\)
• On the Feigenbaum's functional equation \(f^ p(\lambda x)=\lambda f(x)\)
• A complete proof of the Feigenbaum conjectures
• Quantitative universality for a class of nonlinear transformations
• Fixed points of composition operators. II
• Solutions for the p-order Feigenbaum's functional equation h(g(x))=g^p(h(x))
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