@article{Abramov_2024, title={Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices}, volume={76}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/7324}, DOI={10.3842/umzh.v76i3.7324}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>UDC 517.9</p> </div> </div> </div> <p>In [V. M. Abramov, <em>Bull. Austral. Math. Soc.,</em> <strong>104</strong>, 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<span class="Apple-converted-space"> </span>for the existence of a positive solution in the general case.<span class="Apple-converted-space"> </span>The presented proof is based on the application of a version of the<span class="Apple-converted-space"> </span>M. A. Krasnosel’ski fixed-point theorem. The results are then extended to the equations with infinite matrices of a general type.</p>}, number={3}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Abramov, Vyacheslav M.}, year={2024}, month={Mar.}, pages={315–325} }