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Demonstratio Mathematica

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Volume 47, Issue 3


Single-Valley-Extended Continuous Solutions For The Feigenbaum’S Functional Equation ƒ(ϕ(x))=ϕ2(f(x))

Min Zhang
Published Online: 2014-09-02 | DOI: https://doi.org/10.2478/dema-2014-0049


This work deals with the Feigenbaum’s functional equation in the broad sense

where ϕ2 is the 2-fold iteration of ϕ f(x) is a strictly increasing continuous function on r0; 1s and satisfies f(0)=0; f(x) <x; x Ɛ (0, 1]). Using constructive method, we discuss the existence of single-valley-extended continuous solutions of the above equation.

Keywords: and phrases: functional equation; constructive method; initial function; single-valley-extended continuous solutions


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About the article

Received: 2012-12-26

Revised: 2013-08-06

Published Online: 2014-09-02

Published in Print: 2014-07-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 3, Pages 615–626, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0049.

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© by Min Zhang. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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