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

IF 0.5 4区数学 Q3 MATHEMATICS

Ukrainian Mathematical Journal 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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来源期刊

Ukrainian Mathematical Journal MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

107

审稿时长

4-8 weeks

期刊介绍： Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries. Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.