On dominant contractions and a generalization of the zero-two law

Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m) be two positive contractions such that $T\leq S$. If $\|S-T\|<1$ then $\|S^n-T^n\|<1$ for all n\in\bn. In the present paper we generalize this result to multi-parameter contractions acting on $L^1$. As an application of that result we prove a generalization of the "zero-two" law.Comment: 10 page

Fortet-Mourier norms associated with some iterated function systems

We extend a criterion for the existence of attractive probability measures for iterated function systems which we have obtained recently. In the proof of our extension we have developed a line of investigations suggested by Lasota and Yorke (1994. Random Comput. Dyn. 2, 41-77)