IJPAM: Volume 26, No. 3 (2006)

ON CONJUGACY EQUATIONS FOR
ITERATIVE FUNCTIONAL EQUATIONS

Jitka Laitochová
Department of Mathematics, PdF
Palacký University
Zizkovo nám. 5, Olomouc, 771 40, CZECH REPUBLIC
e-mail: jitka.laitochova@upol.cz


Abstract.The paper studies conjugacy equations $\alpha (f(x))=g(\alpha(x))$, which are used to convert iterative functional equations to simpler forms. The functions $f$ and $g$ are given, with $g$ especially simple, e.g., $g(x)=x+1$ in the case of Abel's functional equation. An iterative construction is given for infinitely many monotonic solutions $\alpha$. The recursive algorithm can be implemented in computer algebra systems.

Received: February 6, 2006

AMS Subject Classification: 39B05, 39B12

Key Words and Phrases: conjugacy equations, iterative functional equations, phase function, iteration, fundamental central dispersion, Abel functional equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 3