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arXiv · 2202.05438

Fixed point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices

Vyacheslav M. Abramov
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Abstract

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.

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Vyacheslav M. Abramov. 2022-02-11. Fixed point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices. https://arxiv.org/abs/2202.05438

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