We define two functions f and g on the unit interval [0, 1] to be strongly conjugate $\operatorname {iff}$ there is an order-preserving homeomorphism h of [0, 1] such that g = h -1 fh (a minor ...

Asher Tishler, Isreal Zang, A Maximum Likelihood Method for Piecewise Regression Models with a Continuous Dependent Variable, Journal of the Royal Statistical Society.