HYERS-ULAM-RASSIAS TYPE STABILITY OF POLYNOMIAL EQUATIONS

Abstract

In this paper we introduce the concept of Hyers-Ulam-Rassias stability of polynomial equations and then we show that if x is an approximate solution of the equation anxn + an􀀀1xn􀀀1 + :::a1x + a0, then there exists an exact solution of the equation near to x.

Keywords

• Hyers-Ulam stability,Hyers-Ulam-Rassias stability; Polynomial equa- tion; power series equation

References

1. [1] M. Bikhdam, H. A. Soleiman Mezerji and M. Eshaghi Gordji, Hyers-Ulam stability of power series equations, Abstract and Applied Analysis, Vol: 2011 (2011), 6 pages.
2. [2] Y. Li and L.Hua, Hyers-Ulam stability of a polynomial equation, Banach J. Math. Anal. Vol: 3, No. 2 (2009), 86{90.
3. [3] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., U.S.A. Vol: 27 (1941), 222{224.
4. [4] D.H. Hyers, G.Isac and Th.M. Rassias, Stability of functional equations in several variables, Birkhauser, Basel, 1998.
5. [5] D.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequationes Math. Vol: 44, No. 2-3 (1992), 125{153.
6. [6] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., Vol: 6 (1978), 297{300.
7. [7] S. M. Ulam, Problems in modern mathematics, Chap. VI, Science eds., Wiley, New-York, 1960.