Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland
Copyright © 2009 Krzysztof Ciepliński and Marek Cezary 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.
We investigate the existence and uniqueness of solutions of the functional equation , , where are closed intervals, and , are some
continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.