Aequationes mathematicae

, Volume 93, Issue 1, pp 149–160 | Cite as

The geometric rate of convergence of random iteration in the Hutchinson distance

  • Rafał KapicaEmail author
Open Access


Using the Banach fixed-point theorem we provide a simple criterion of the geometric rate of convergence and of asymptotic stability of Markov operators in the Hutchinson distance. The obtained results are applied to sequences of iterates of random-valued functions.


Markov operators Random-valued functions Random iteration Asymptotic stability Rate of convergence 

Mathematics Subject Classification

Primary 60J05 Secondary 37A99 



This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education.


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland

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