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On the Stability of Polynomial Equations

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Abbas Najati

    (University of Mohaghegh Ardabili)

  • Themistocles M. Rassias

    (National Technical University of Athens)

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.

Suggested Citation

  • Abbas Najati & Themistocles M. Rassias, 2011. "On the Stability of Polynomial Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 223-227, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_18
    DOI: 10.1007/978-1-4614-0055-4_18
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    Keywords

    Hyers-Ulam stability; Polynomial equation;

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