STABILITY OF ZEROS OF POWER SERIES EQUATIONS

Abstract

We prove that if vertical bar a(1)vertical bar is large and vertical bar a(0)vertical bar is small enough, then every approximate zero of power series equation Sigma(infinity)(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) + . . . + a(1)z + a(0) = 0 for a given integer n > 1.