On zero distribution of a class of continuous functions^∗

^∗This work is supported in part by the Foundation of Zhongshan University Advanced Research Centre.

Abstract

Kuhn's rootfinding algorithm is revised to be a zerofinding algorithm for any continuous complex function in one complex variable. A sufficient condition for the convergence is set up, and it leads to a result on zero distribution of a class of continuous functions. More concretely, this paper supplies a constructive proof to the following theorem: Suppose f(Z) is a continuous complex function in one complex variable and there exists a positive integer n, a complex Z₀ , a nonzero complex a and a positive r such that lim and |Z–Z₀0|> r implies then the algebraic number of zeros of f(z) inside |z—z₀ |≤ r is at least n

AMS (MOS):

• 30C15
• 65H05

^∗This work is supported in part by the Foundation of Zhongshan University Advanced Research Centre.

^∗This work is supported in part by the Foundation of Zhongshan University Advanced Research Centre.

Notes

^∗This work is supported in part by the Foundation of Zhongshan University Advanced Research Centre.