On the surjectivity of quadratic stochastic operators acting on the simplex
It is well-known that a linear stochastic operator (a Markov operator) associated with a square stochastic matrix is a surjection of the simplex if and only if it is bijective. The similar problem was open for nonlinear stochastic operators (nonlinear Markov operators) associated with stochastic hy...
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| Format: | Article |
| Language: | English English English |
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Pleiades Publishing
2016
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| Online Access: | http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/1/Surjective_QSO_---_MN_%28Eng%29.pdf http://irep.iium.edu.my/51164/4/51164-On_the_surjectivity_of_quadratic_stochastic_operators_SCOPUS.pdf http://irep.iium.edu.my/51164/5/51164-On_the_surjectivity_of_quadratic_stochastic_operators_WOS.pdf |
| _version_ | 1848783797069283328 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | It is well-known that a linear stochastic operator (a
Markov operator) associated with a square stochastic matrix is a surjection of the simplex if and only if it is bijective. The similar problem was open for nonlinear stochastic operators (nonlinear Markov operators) associated with stochastic hyper-matrices (higher dimensional matrices). In this paper, we solved this problem for quadratic stochastic operators acting on the simplex. Namely, we showed that a quadratic stochastic operator associated with a cubic stochastic matrix is a surjection of the simplex if and only if
it is bijective. Moreover, we also described all surjective quadratic stochastic operators of the simplex. |
| first_indexed | 2025-11-14T16:27:03Z |
| format | Article |
| id | iium-51164 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T16:27:03Z |
| publishDate | 2016 |
| publisher | Pleiades Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-511642016-12-22T06:42:54Z http://irep.iium.edu.my/51164/ On the surjectivity of quadratic stochastic operators acting on the simplex Saburov, Mansoor QA Mathematics It is well-known that a linear stochastic operator (a Markov operator) associated with a square stochastic matrix is a surjection of the simplex if and only if it is bijective. The similar problem was open for nonlinear stochastic operators (nonlinear Markov operators) associated with stochastic hyper-matrices (higher dimensional matrices). In this paper, we solved this problem for quadratic stochastic operators acting on the simplex. Namely, we showed that a quadratic stochastic operator associated with a cubic stochastic matrix is a surjection of the simplex if and only if it is bijective. Moreover, we also described all surjective quadratic stochastic operators of the simplex. Pleiades Publishing 2016-03 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51164/1/Surjective_QSO_---_MN_%28Eng%29.pdf application/pdf en http://irep.iium.edu.my/51164/4/51164-On_the_surjectivity_of_quadratic_stochastic_operators_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/51164/5/51164-On_the_surjectivity_of_quadratic_stochastic_operators_WOS.pdf Saburov, Mansoor (2016) On the surjectivity of quadratic stochastic operators acting on the simplex. Mathematical Notes, 99 (3-4). pp. 623-627. ISSN 0001-4346 E-ISSN 1573-8876 http://link.springer.com/article/10.1134/S0001434616030391 10.1134/S0001434616030391 |
| spellingShingle | QA Mathematics Saburov, Mansoor On the surjectivity of quadratic stochastic operators acting on the simplex |
| title | On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_full | On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_fullStr | On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_full_unstemmed | On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_short | On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_sort | on the surjectivity of quadratic stochastic operators
acting on the simplex |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/1/Surjective_QSO_---_MN_%28Eng%29.pdf http://irep.iium.edu.my/51164/4/51164-On_the_surjectivity_of_quadratic_stochastic_operators_SCOPUS.pdf http://irep.iium.edu.my/51164/5/51164-On_the_surjectivity_of_quadratic_stochastic_operators_WOS.pdf |