Email this article A counterexample to the stochastic version of the Brouwer fixed point theorem
- Authors: Ponosov A.V.1
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Affiliations:
- Norwegian University of Life Sciences
- Issue: Vol 26, No 134 (2021)
- Pages: 143-150
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/294985
- DOI: https://doi.org/10.20310/2686-9667-2021-26-134-143-150
- ID: 294985
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Abstract
It is shown that the stochastic counterpart of the classical fixed point theorem for continuous maps in a finite dimensional Euclidean space (“Brouwer’s theorem”) is not, in general, true. This result implies, in particular, that a careful choice of invariant sets in the stochastic version of Brouwer’s theorem is necessary in the theory of stochastic nonlinear operators.
About the authors
Arcady V. Ponosov
Norwegian University of Life Sciences
Email: arkadi@nmbu.no
Doctor of Natural Sciences, Professor of the Institute of Mathematics P.O. Box 5003, №-1432, ˚As 5003, Norway
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