Report Number: CS-TR-69-137
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