TY - JOUR
AU - Vyacheslav M. Abramov
PY - 2024/03/25
Y2 - 2024/04/14
TI - Fixed-point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 76
IS - 3
SE - Research articles
DO - 10.3842/umzh.v76i3.7324
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/7324
AB - UDC 517.9In [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.
ER -