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

  • Vyacheslav M. Abramov 24 Sagan Drive, Cranbourne North, Victoria, Australia
Keywords: Banach space, fixed point theorem, Krasnoselskii's fixed point theorem, operator equation, Toeplitz matrix


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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How to Cite
Abramov, V. M. “Fixed-Point Theorem for an Infinite Toeplitz Matrix and Its Extension to General Infinite Matrices”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, no. 3, Mar. 2024, pp. 315–325, doi:10.3842/umzh.v76i3.7324.
Research articles