Invariant measures of Markov operators associated to iterated function systems consisting of phi-max-contractions with probabilities

TL;DR

This paper proves the existence and uniqueness of an invariant measure for a class of Markov operators linked to iterated function systems made of phi-max-contractions with probabilities, with the measure's support being the system's attractor.

Contribution

It establishes the unique invariant measure for a new class of iterated function systems involving phi-max-contractions, expanding understanding of their probabilistic properties.

Findings

Unique invariant measure exists for the system

Support of the measure coincides with the attractor

Provides theoretical foundation for systems with phi-max-contractions

Abstract

We prove that the Markov operator associated to an iterated function system consisting of phi-max-contractions with probabilities has a unique invariant measure whose support is the attractor of the system.