Institution: Stanford University, Department of Computer Science

Title: Fixed points of analytic functions

Author: Henrici, Peter

Date: July 1969

Abstract: A continuous mapping of a simply connected, closed, bounded set of the euclidean plane into itself is known to have at least one fixed point. It is shown that the usual condition for the fixed point to be unique, and for convergence of the iteration sequence to the fixed point, can be relaxed if the mapping is defined by an analytic function of a complex variable.

http://i.stanford.edu/pub/cstr/reports/cs/tr/69/137/CS-TR-69-137.pdf