无穷托普利兹矩阵的定点定理及其对一般无穷矩阵的扩展

Pub Date : 2024-09-06 DOI:10.1007/s11253-024-02324-9

Vyacheslav M. Abramov

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引用次数: 0

摘要

在[V. M. Abramov, Bull. Austral. Math. Soc., 104, 108 (2021)]中，研究了无限非负特定托普利兹矩阵的定点方程。在本研究中，我们提供了在一般情况下存在正解的另一种证明。该证明基于 M. A. Krasnosel'skii 定点定理版本的应用。然后将结果推广到一般类型的无限矩阵方程。

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Fixed-Point Theorem for an Infinite Toeplitz Matrix and Its Extension to General Infinite Matrices

In [V. M. Abramov, Bull. Austral. Math. Soc., 104, 108 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present work, we provide an alternative proof of the existence of a positive solution in the general case. This proof is based on the application of a version of the M. A. Krasnosel’skii fixed-point theorem. The results are then extended to the equations with infinite matrices of the general type.

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