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Hyers-Ulam stability of a polynomial equation. (English) Zbl 1192.39022

The authors prove a Hyers-Ulam type stability result for the polynomial equation x n +αx+β=0. In particular, using Banach’s contraction mapping theorem, they prove the following result: If |α|>n, |β|<|α|-1 and y[-1,1] satisfies the inequality

|y n +αy+β|ε

for some ϵ>0 and for all y[-1,1], then there exists a solution v[-1,1] of x n +αx+β=0 such that

|y-v|kε,

where k is a positive constant.


MSC:
39B82Stability, separation, extension, and related topics
39B22Functional equations for real functions