Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 230414, 11 pages
doi:10.1155/2009/230414
Research Article

On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions

Krzysztof Ciepliński and Marek Cezary Zdun

Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Received 23 December 2008; Accepted 24 June 2009

Academic Editor: Lech Górniewicz

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.

Abstract

We investigate the existence and uniqueness of solutions φ:I→J of the functional equation φ(f(x))=F(φ(x)), 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.