an: Zbl 1192.39022
au: Li, Yongjin; Hua, Liubin
ti: Hyers-Ulam stability of a polynomial equation.
la: EN
so: Banach J. Math. Anal. 3, No. 2, 86-90, electronic only (2009).
py: 2009
dt: J
cc: *39B82 39B22
ut: Hyers-Ulam stability; polynomial equation
ab: 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.
rv: Prasanna Sahoo (Louisville)