Zhihua Wang, Xiuming Dong, Themistocles M. Rassias, and Soon-Mo Jung Hubei University of Technology, Hubei University of Technology, National Technical University of Athens, Hongik University

Abstract : We prove that if $| a_1 |$ is large and $| a_0 |$ is small enough, then every approximate zero of power series equation $\sum^{\infty}_{n=0} a_n x^n = 0$ can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree $n$, $a_n z^n + a_{n-1} z^{n-1} + \cdots + a_1 z + a_0 = 0$ for a given integer $n > 1$.

Keywords : Hyers-Ulam stability, power series equation, polynomial equation, zero