Invariant measures of Markov operators associated to iterated function systems consisting of \(\varphi\)-max-contractions with probabilities (Q1629139)

The authors consider iterated function systems (IFSs) whose maps are so-called \(\varphi\)-max-contractions. They study the Markov operators associated with this type of IFS with probabilities and show that each such operator has a unique attractor which is the support of a unique invariant measure. The existence of this invariant measure follows from the Riesz representation theorem applied to a positive linear functional which is generated by the dual operator of the Markov operator.