@article{1192.39022,
author="Li, Yongjin and Hua, Liubin",
title="{Hyers-Ulam stability of a polynomial equation.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="3",
number="2",
pages="86-90",
year="2009",
abstract="{The authors prove a Hyers-Ulam type stability result for the
    polynomial equation $x^n + \alpha x + \beta = 0$. In particular, using
    Banach's contraction mapping theorem, they prove the following result: If $
    |\alpha | > n$, $|\beta | < |\alpha|-1$ and $y \in [-1, 1]$ satisfies the
    inequality 
 $$|y^n + \alpha y + \beta | \leq \varepsilon $$ 
 for some
    $\epsilon > 0$ and for all $y \in [-1, 1]$, then there exists a solution $v
    \in [-1, 1]$ of $x^n + \alpha x +\beta = 0$ such that 
 $$|y-v| \leq k
    \varepsilon, $$ 
 where $k$ is a positive constant.}",
reviewer="{Prasanna Sahoo (Louisville)}",
keywords="{Hyers-Ulam stability; polynomial equation}",
classmath="{*39B82 (Stability, separation, extension, and related topics)
39B22 (Functional equations for real functions)
}",
}