Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices
UDC 517.9 In [V. M. Abramov, Bull. Austral. Math. Soc., 104, 108–117 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present paper, we provide an alternative proof  for the existence of a positi...
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Institute of Mathematics, NAS of Ukraine
2024
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| author | Abramov, Vyacheslav M. Abramov, Vyacheslav M. |
| author_facet | Abramov, Vyacheslav M. Abramov, Vyacheslav M. |
| author_sort | Abramov, Vyacheslav M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:17Z |
| description |
UDC 517.9
In [V. M. Abramov, Bull. Austral. Math. Soc., 104, 108–117 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present paper, we provide an alternative proof  for the existence of a positive solution in the general case. The presented proof is based on the application of a version of the  M. A. Krasnosel'ski fixed-point theorem. The results are then extended to the equations with infinite matrices of a general type. |
| doi_str_mv | 10.3842/umzh.v76i3.7324 |
| first_indexed | 2026-03-24T03:32:11Z |
| format | Article |
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| id | umjimathkievua-article-7324 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:11Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-73242024-06-19T00:35:17Z Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices Abramov, Vyacheslav M. Abramov, Vyacheslav M. Banach space fixed point theorem Krasnoselskii's fixed point theorem operator equation Toeplitz matrix UDC 517.9 In [V. M. Abramov, Bull. Austral. Math. Soc., 104, 108–117 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present paper, we provide an alternative proof  for the existence of a positive solution in the general case. The presented proof is based on the application of a version of the  M. A. Krasnosel'ski fixed-point theorem. The results are then extended to the equations with infinite matrices of a general type. УДК 517.9 Tеорема про нерухому точку для нескінченної матриці Tепліца та її поширення на загальні нескінченні матриці  У [V. M. Abramov, Bull. Austral. Math. Soc., 104, 108–117 (2021)] досліджено рівняння з нерухомою точкою для нескінченної невід'ємної особливої матриці Тепліца. У цій статті ми наводимо альтернативне доведення існування додатного розв'язку в загальному випадку. Наведене доведення ґрунтується на застосуванні варіанту теореми  М. О. Красносельського про нерухому точку. Результати поширено на рівняння з нескінченними матрицями загального вигляду.  Institute of Mathematics, NAS of Ukraine 2024-03-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7324 10.3842/umzh.v76i3.7324 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 3 (2024); 315–325 Український математичний журнал; Том 76 № 3 (2024); 315–325 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7324/9849 Copyright (c) 2024 Vyacheslav Abramov |
| spellingShingle | Abramov, Vyacheslav M. Abramov, Vyacheslav M. Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices |
| title | Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices |
| title_alt | Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices |
| title_full | Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices |
| title_fullStr | Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices |
| title_full_unstemmed | Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices |
| title_short | Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices |
| title_sort | fixed-point theorem for an infinite toeplitz matrix and its extension to general infinite matrices |
| topic_facet | Banach space fixed point theorem Krasnoselskii's fixed point theorem operator equation Toeplitz matrix |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7324 |
| work_keys_str_mv | AT abramovvyacheslavm fixedpointtheoremforaninfinitetoeplitzmatrixanditsextensiontogeneralinfinitematrices AT abramovvyacheslavm fixedpointtheoremforaninfinitetoeplitzmatrixanditsextensiontogeneralinfinitematrices |