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

Vyacheslav M. Abramov

doi:10.3842/umzh.v76i3.7324

Vyacheslav M. Abramov 24 Sagan Drive, Cranbourne North, Victoria, Australia

DOI: https://doi.org/10.3842/umzh.v76i3.7324

Keywords: Banach space, fixed point theorem, Krasnoselskii's fixed point theorem, operator equation, Toeplitz matrix

Abstract

UDC 517.9

In [V. M. Abramov, Bull. Austral. Math. Soc., 104, 108–117 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present paper, we provide an alternative proof for the existence of a positive solution in the general case. The presented proof is based on the application of a version of the M. A. Krasnosel'ski fixed-point theorem. The results are then extended to the equations with infinite matrices of a general type.

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