an:05702389 Zbl 1192.39022 Li, Yongjin; Hua, Liubin Hyers-Ulam stability of a polynomial equation. EN Banach J. Math. Anal. 3, No. 2, 86-90, electronic only (2009). ISSN 1735-8787/e 2009

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*39B82 39B22 Hyers-Ulam stability; polynomial equation 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. Prasanna Sahoo (Louisville)