On regularity of diagonally positive quadratic doubly stochastic operators
The classical Perron–Frobenius theorem says that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix always converges to a unique fixed point. In general, an analogy of the Perron–Frobenius theorem does not hold for a quadratic stochastic operator associa...
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| Format: | Article |
| Language: | English English |
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Springer International Publishing AG
2017
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| Online Access: | http://irep.iium.edu.my/59920/ http://irep.iium.edu.my/59920/1/Regularity%20QDSO%20---RiM.pdf http://irep.iium.edu.my/59920/7/On%20regularity%20of%20diagonally%20positive%20quadratic%20doubly%20stochastic%20operators.pdf |
| _version_ | 1848785400742543360 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | The classical Perron–Frobenius theorem says that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix always converges to a unique fixed point. In general, an analogy of the Perron–Frobenius theorem does not hold for a quadratic stochastic operator associated with a positive cubic stochastic matrix. Namely, its trajectories may converge to different fixed points depending on initial points or may not converge at all. In this paper, we show regularity of quadratic doubly stochastic operators associated with diagonally positive cubic stochastic matrices. This is a nonlinear analogy of the Perron–Frobenius theorem for positive doubly stochastic matrices. |
| first_indexed | 2025-11-14T16:52:33Z |
| format | Article |
| id | iium-59920 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:52:33Z |
| publishDate | 2017 |
| publisher | Springer International Publishing AG |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-599202018-03-13T08:24:19Z http://irep.iium.edu.my/59920/ On regularity of diagonally positive quadratic doubly stochastic operators Saburov, Mansoor QA Mathematics The classical Perron–Frobenius theorem says that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix always converges to a unique fixed point. In general, an analogy of the Perron–Frobenius theorem does not hold for a quadratic stochastic operator associated with a positive cubic stochastic matrix. Namely, its trajectories may converge to different fixed points depending on initial points or may not converge at all. In this paper, we show regularity of quadratic doubly stochastic operators associated with diagonally positive cubic stochastic matrices. This is a nonlinear analogy of the Perron–Frobenius theorem for positive doubly stochastic matrices. Springer International Publishing AG 2017-07-18 Article PeerReviewed application/pdf en http://irep.iium.edu.my/59920/1/Regularity%20QDSO%20---RiM.pdf application/pdf en http://irep.iium.edu.my/59920/7/On%20regularity%20of%20diagonally%20positive%20quadratic%20doubly%20stochastic%20operators.pdf Saburov, Mansoor (2017) On regularity of diagonally positive quadratic doubly stochastic operators. Results in Mathematics, 72 (4). pp. 1907-1918. ISSN 1422-6383 https://link.springer.com/article/10.1007/s00025-017-0723-3 10.1007/s00025-017-0723-3 |
| spellingShingle | QA Mathematics Saburov, Mansoor On regularity of diagonally positive quadratic doubly stochastic operators |
| title | On regularity of diagonally positive quadratic doubly stochastic operators |
| title_full | On regularity of diagonally positive quadratic doubly stochastic operators |
| title_fullStr | On regularity of diagonally positive quadratic doubly stochastic operators |
| title_full_unstemmed | On regularity of diagonally positive quadratic doubly stochastic operators |
| title_short | On regularity of diagonally positive quadratic doubly stochastic operators |
| title_sort | on regularity of diagonally positive quadratic doubly stochastic operators |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/59920/ http://irep.iium.edu.my/59920/ http://irep.iium.edu.my/59920/ http://irep.iium.edu.my/59920/1/Regularity%20QDSO%20---RiM.pdf http://irep.iium.edu.my/59920/7/On%20regularity%20of%20diagonally%20positive%20quadratic%20doubly%20stochastic%20operators.pdf |