Fixed point of some Markov operator of Frobenius-Perron type generated by a random family of point-transformations in ℝ<superscript>d</superscript>.
In: Advances in Nonlinear Analysis, Jg. 10 (2021), Heft 1, S. 972-981
Online
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Zugriff:
Existence of fixed point of a Frobenius-Perron type operator P : L1 ⟶ L1 generated by a family {φy}y∈Y of nonsingular Markov maps defined on a σ-finite measure space (I, Σ, m) is studied. Two fairly general conditions are established and it is proved that they imply for any g ∈ G = {ƒ ∈ L1 : ƒ ≥ 0, and ∥ƒ∥ = 1}, the convergence (in the norm of L1) of the sequence {Pjg}j=1∞ to a unique fixed point g0. The general result is applied to a family of C1+α-smooth Markov maps in ℝd. [ABSTRACT FROM AUTHOR]
| Titel: |
Fixed point of some Markov operator of Frobenius-Perron type generated by a random family of point-transformations in ℝ<superscript>d</superscript>.
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| Autor/in / Beteiligte Person: | Bugiel, Peter ; Wędrychowicz, Stanisław ; Rzepka, Beata |
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| Zeitschrift: | Advances in Nonlinear Analysis, Jg. 10 (2021), Heft 1, S. 972-981 |
| Veröffentlichung: | 2021 |
| Medientyp: | academicJournal |
| ISSN: | 2191-9496 (print) |
| DOI: | 10.1515/anona-2020-0163 |
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