On the Stability of Polynomial Equations

Abbas Najati () and Themistocles M. Rassias ()
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Abbas Najati: University of Mohaghegh Ardabili
Themistocles M. Rassias: National Technical University of Athens

Chapter Chapter 18 in Functional Equations in Mathematical Analysis, 2011, pp 223-227 from Springer

Abstract: Abstract In this article we prove the Hyers–Ulam type stability for the following two equations with real coefficients: $${a}_{n}{x}^{n} + {a}_{ n-1}{x}^{n-1} + \cdots + {a}_{ 1}x + {a}_{0} = 0\quad \mbox{ and }\quad {e}^{x} + \alpha x + \beta = 0$$ on a real interval [a, b]. More precisely, we show that if x is an approximate solution of the equation $${a}_{n}{x}^{n} + {a}_{n-1}{x}^{n-1} + \cdots + {a}_{1}x + {a}_{0} = 0$$ (resp. $${e}^{x} + \alpha x + \beta = 0)$$ , then there exists an exact solution of the equation near x.

Keywords: Hyers-Ulam stability; Polynomial equation (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0055-4_18

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DOI: 10.1007/978-1-4614-0055-4_18

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