Hyers-Ulam stability of the first-order matrix difference equations

In this paper, we prove the Hyers-Ulam stability of the first-order linear homogeneous matrix difference equations x→i=Ax→i−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{x}_{i} = \mathbf{A} \vec{x}_{i-1}$\end{document} and x→i−1=Ax→i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{x}_{i-1} = \mathbf{A} \vec{x}_{i}$\end{document} for all integers i∈Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$i \in\mathbf{Z}$\end{document}.