{"title":"Fixed-Point Theorem for an Infinite Toeplitz Matrix and Its Extension to General Infinite Matrices","authors":"Vyacheslav M. Abramov","doi":"10.1007/s11253-024-02324-9","DOIUrl":null,"url":null,"abstract":"<p>In [V. M. Abramov, <i>Bull. Austral. Math. Soc.</i>, <b>104</b>, 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.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02324-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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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