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Projective surjectivity of quadratic stochastic operators on L1 and its application

A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over an infinite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) d...

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Main Authors:	Mukhamedov, F., Khakimov, O., Embong, A. F.
Format:	Article
Language:	English
Published:	Elsevier Ltd. 2021
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/96514/1/AFadillahEmbong2021_ProjectiveSurjectivityofQuadraticStochastic.pdf http://eprints.utm.my/id/eprint/96514/ http://dx.doi.org/10.1016/j.chaos.2021.111034
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spelling	my.utm.965142022-07-26T08:03:31Z http://eprints.utm.my/id/eprint/96514/ Projective surjectivity of quadratic stochastic operators on L1 and its application Mukhamedov, F. Khakimov, O. Embong, A. F. QA Mathematics A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over an infinite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex). In the present paper, we consider a continuous analogue of the mentioned mapping acting on L1-spaces. Main aim of the current paper is to investigate projective surjectivity of quadratic stochastic operators (QSO) acting on the set of all probability measures. To prove the main result, we study the surjectivity of infinite dimensional nonlinear Markov operators and apply them to the projective surjectivity of the considered QSO. Furthermore, the obtained results are applied to the existence of the positive solution of some Hammerstein integral equations. Elsevier Ltd. 2021 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/96514/1/AFadillahEmbong2021_ProjectiveSurjectivityofQuadraticStochastic.pdf Mukhamedov, F. and Khakimov, O. and Embong, A. F. (2021) Projective surjectivity of quadratic stochastic operators on L1 and its application. Chaos, Solitons and Fractals, 148 (NA). p. 111034. ISSN 0960-0779 http://dx.doi.org/10.1016/j.chaos.2021.111034 DOI: 10.1016/j.chaos.2021.111034
institution	Universiti Teknologi Malaysia
building	UTM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Teknologi Malaysia
content_source	UTM Institutional Repository
url_provider	http://eprints.utm.my/
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Mukhamedov, F. Khakimov, O. Embong, A. F. Projective surjectivity of quadratic stochastic operators on L1 and its application
description	A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over an infinite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex). In the present paper, we consider a continuous analogue of the mentioned mapping acting on L1-spaces. Main aim of the current paper is to investigate projective surjectivity of quadratic stochastic operators (QSO) acting on the set of all probability measures. To prove the main result, we study the surjectivity of infinite dimensional nonlinear Markov operators and apply them to the projective surjectivity of the considered QSO. Furthermore, the obtained results are applied to the existence of the positive solution of some Hammerstein integral equations.
format	Article
author	Mukhamedov, F. Khakimov, O. Embong, A. F.
author_facet	Mukhamedov, F. Khakimov, O. Embong, A. F.
author_sort	Mukhamedov, F.
title	Projective surjectivity of quadratic stochastic operators on L1 and its application
title_short	Projective surjectivity of quadratic stochastic operators on L1 and its application
title_full	Projective surjectivity of quadratic stochastic operators on L1 and its application
title_fullStr	Projective surjectivity of quadratic stochastic operators on L1 and its application
title_full_unstemmed	Projective surjectivity of quadratic stochastic operators on L1 and its application
title_sort	projective surjectivity of quadratic stochastic operators on l1 and its application
publisher	Elsevier Ltd.
publishDate	2021
url	http://eprints.utm.my/id/eprint/96514/1/AFadillahEmbong2021_ProjectiveSurjectivityofQuadraticStochastic.pdf http://eprints.utm.my/id/eprint/96514/ http://dx.doi.org/10.1016/j.chaos.2021.111034
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score	13.211869

Projective surjectivity of quadratic stochastic operators on L1 and its application

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