Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel
Positive fixed points of the Hammerstein integral operators with a degenerate kernel in the space of continuous functions C [0, 1] were explored. The problem of determining the number of positive fixed points of the Hammerstein integral operator was reduced to analyzing the positive roots of polynomia...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-10-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/102 |
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| _version_ | 1849316326687899648 |
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| author | Yu. Kh. Eshkabilov Sh. D. Nodirov |
| author_facet | Yu. Kh. Eshkabilov Sh. D. Nodirov |
| author_sort | Yu. Kh. Eshkabilov |
| collection | DOAJ |
| description | Positive fixed points of the Hammerstein integral operators with a degenerate kernel in the space of continuous functions C [0, 1] were explored. The problem of determining the number of positive fixed points of the Hammerstein integral operator was reduced to analyzing the positive roots of polynomials with real coefficients. A model on a Cayley tree with nearestneighbor interactions and with the set [0, 1] of spin values was considered. It was proved that a unique translation-invariant Gibbs measure exists for this model. |
| format | Article |
| id | doaj-art-9f097c9d1a43432b8485c04e82aaa4b4 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-9f097c9d1a43432b8485c04e82aaa4b42025-08-20T03:51:48ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-10-01166343744910.26907/2541-7746.2024.3.437-44960Positive Fixed Points of Hammerstein Integral Operators with Degenerate KernelYu. Kh. Eshkabilov0Sh. D. Nodirov1Tashkent International University of Financial Management and TechnologiesKarshi State UniversityPositive fixed points of the Hammerstein integral operators with a degenerate kernel in the space of continuous functions C [0, 1] were explored. The problem of determining the number of positive fixed points of the Hammerstein integral operator was reduced to analyzing the positive roots of polynomials with real coefficients. A model on a Cayley tree with nearestneighbor interactions and with the set [0, 1] of spin values was considered. It was proved that a unique translation-invariant Gibbs measure exists for this model.https://uzakufismat.elpub.ru/jour/article/view/102fixed pointhammerstein integral operatorcayley treegibbs measuretranslation-invariant gibbs measure |
| spellingShingle | Yu. Kh. Eshkabilov Sh. D. Nodirov Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel Учёные записки Казанского университета: Серия Физико-математические науки fixed point hammerstein integral operator cayley tree gibbs measure translation-invariant gibbs measure |
| title | Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel |
| title_full | Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel |
| title_fullStr | Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel |
| title_full_unstemmed | Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel |
| title_short | Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel |
| title_sort | positive fixed points of hammerstein integral operators with degenerate kernel |
| topic | fixed point hammerstein integral operator cayley tree gibbs measure translation-invariant gibbs measure |
| url | https://uzakufismat.elpub.ru/jour/article/view/102 |
| work_keys_str_mv | AT yukheshkabilov positivefixedpointsofhammersteinintegraloperatorswithdegeneratekernel AT shdnodirov positivefixedpointsofhammersteinintegraloperatorswithdegeneratekernel |