Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 230414, 11 pages
doi:10.1155/2009/230414
On uniqueness of conjugacy of continuous and piecewise monotone functions
Krzysztof Ciepliński
and Marek Cezary Zdun
Institute of Mathematics, Pedagogical University, Podchor\c{a}żych 2, 30-084 Kraków, Poland
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.