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Dichotomy of Iterated Means for Nonlinear Operators

Abstract

In this paper, we discuss a dichotomy of iterated means of nonlinear operators acting on a compact convex subset of a finite-dimensional real Banach space. As an application, we study the mean ergodicity of nonhomogeneous Markov chains.

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Correspondence to M. Saburov.

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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 1, pp. 89–91, 2018

Original Russian Text Copyright © by M. Saburov

This work was partially supported by the MOHE grant FRGS14-141-0382. The author also thanks the Junior Associate Scheme, Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy, where this paper was written, for invitation and hospitality.

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Saburov, M. Dichotomy of Iterated Means for Nonlinear Operators. Funct Anal Its Appl 52, 74–76 (2018). https://doi.org/10.1007/s10688-018-0212-9

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  • DOI: https://doi.org/10.1007/s10688-018-0212-9

Key words

  • mean ergodicity
  • iterated means
  • nonhomogeneous Markov chain