On uniqueness of fixed points of positive quadratic stochastic operators
We know from the theory of Markov chains that any positive square stochastic matrix has a unique fixed point in the simplex and its trajectory starting from any initial point of the simplex converges to that unique fixed point. However, in general, the similar result for a positive cubic stochastic...
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| Format: | Proceeding Paper |
| Language: | English |
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2015
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| Online Access: | http://irep.iium.edu.my/46251/ http://irep.iium.edu.my/46251/4/ID46251.pdf |
| _version_ | 1848782933849014272 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | We know from the theory of Markov chains that any positive square stochastic matrix has a unique fixed point in the simplex and its trajectory starting from any initial point of the simplex converges to that unique fixed point. However, in general, the similar result for a positive cubic stochastic matrix does not hold true. We know that a cubic stochastic matrix is associated with a quadratic stochastic operator defined on the simplex. In this paper, we provide a uniqueness criterion for fixed points of positive quadratic stochastic operators defined on 2D simplex. |
| first_indexed | 2025-11-14T16:13:20Z |
| format | Proceeding Paper |
| id | iium-46251 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:13:20Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-462512018-05-21T05:35:23Z http://irep.iium.edu.my/46251/ On uniqueness of fixed points of positive quadratic stochastic operators Saburov, Mansoor QA Mathematics We know from the theory of Markov chains that any positive square stochastic matrix has a unique fixed point in the simplex and its trajectory starting from any initial point of the simplex converges to that unique fixed point. However, in general, the similar result for a positive cubic stochastic matrix does not hold true. We know that a cubic stochastic matrix is associated with a quadratic stochastic operator defined on the simplex. In this paper, we provide a uniqueness criterion for fixed points of positive quadratic stochastic operators defined on 2D simplex. 2015 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/46251/4/ID46251.pdf Saburov, Mansoor (2015) On uniqueness of fixed points of positive quadratic stochastic operators. In: The 2nd International Conference on Mathematical Sciences & Computer Engineering, 5-6 Feb 2015, Langkawi, Kedah Darul Aman, Malaysia. http://www.icmsce.net/2015/WB/www.icmsce.net/cms/index.html |
| spellingShingle | QA Mathematics Saburov, Mansoor On uniqueness of fixed points of positive quadratic stochastic operators |
| title | On uniqueness of fixed points of positive quadratic stochastic operators |
| title_full | On uniqueness of fixed points of positive quadratic stochastic operators |
| title_fullStr | On uniqueness of fixed points of positive quadratic stochastic operators |
| title_full_unstemmed | On uniqueness of fixed points of positive quadratic stochastic operators |
| title_short | On uniqueness of fixed points of positive quadratic stochastic operators |
| title_sort | on uniqueness of fixed points of positive quadratic stochastic operators |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/46251/ http://irep.iium.edu.my/46251/ http://irep.iium.edu.my/46251/4/ID46251.pdf |