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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| Дата: | 2024 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7324 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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| DOI: | 10.3842/umzh.v76i3.7324 |