论文标题
无限toeplitz矩阵的固定点定理及其扩展到一般无限矩阵
Fixed point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices
论文作者
论文摘要
在[V。 M. Abramov，\ emph {Bull。奥斯特。数学。 Soc。} \ textbf {104}（2021），108--117]已经研究了无限非模拟toeplitz矩阵的固定点方程。发现存在阳性溶液和有限的阳性解决方案的条件。但是，存在积极解决方案的证明完全是直接的，不承认对更通用的矩阵的扩展。在本说明中，我们为在更普遍的情况下存在积极解决方案提供了另一种证据。提出的证明基于M. A. Krasnoselskii的固定点定理的变体的应用。然后，对于具有一般类型的无限矩阵的方程式，将扩展结果。
In [V. M. Abramov, \emph{Bull. Aust. Math. Soc.} \textbf{104} (2021), 108--117] the fixed point equation for an infinite nonnegative Toeplitz matrix has been studied. It was found the conditions for existence of a positive solution and bounded positive solution. However, the proof of the existence of a positive solution was entirely straightforward, not admitting extensions for more general types of matrices. In the present note, we provide an alternative proof for the existence of a positive solution in more general case. The presented proof is based on an application of a variant of the fixed point theorem of M. A. Krasnoselskii. The results are then extended for the equations with infinite matrices of a general type.
