What is it about?
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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Why is it important?
It solves new problems for linear operator equations, where the norm of operator can be greater than one.
Perspectives
The study shows new perspectives in the area. The study of linear operator equations when the norm is equal to one is pioneering, and it may be a subject for intensive study by other researchers.
Dr Vyacheslav Abramov
Monash University
Read the Original
This page is a summary of: Fixed-Point Theorem for an Infinite Toeplitz Matrix and Its Extension to General Infinite Matrices, Ukrainian Mathematical Journal, August 2024, Springer Science + Business Media,
DOI: 10.1007/s11253-024-02324-9.
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