On the stability of polynomial equations. (English) Zbl 1247.39032
Rassias, Themistocles M. (ed.) et al., Functional equations in mathematical analysis. Dedicated to the memory of Stanisław Marcin Ulam on the occasion of the 100th anniversary of his birth. Berlin: Springer (ISBN 978-1-4614-0054-7/hbk; 978-1-4614-0055-4/ebook). Springer Optimization and Its Applications 52, 223-227 (2011).
Summary: We prove the Hyers-Ulam type stability for the following two equations with real coefficients:
\[
a_nx^n+a_{n-1}x^{n-1}+\dots+a_1x+a_0=0\text{ and }e^x+\alpha x+\beta=0
\]
on a real interval \([a,b]\). More precisely, we show that if \(x\) is an approximate solution of the equation \(a_nx^n+a_{n-1}x^{n-1}+\dots+a_1x+a_0=0\) (resp. \(e^x+\alpha x+\beta=0\)), then there exists an exact solution of the equation near \(x\).
For the entire collection see [Zbl 1225.39001].
For the entire collection see [Zbl 1225.39001].
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B22 | Functional equations for real functions |
