Research Article On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions

We investigate the existence and uniqueness of solutions ϕ: I → J of the functional equation ϕfx Fϕx, x ∈ I, where I, J are closed intervals, and f: I → I, F: J → J are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result. Copyright q 2009 K. Ciepliński and M. C. Zdun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1