Ultrametric Fixed Point Theorems and Applications
by
Erwin Schörner
University of Munich

According to Banach's classical Fixed Point Theorem, any contracting self-mapping of a complete metric space possesses a uniquely determined fixed point.

This result was transferred to spherically complete ultrametric spaces by Prieß-Crampe; this was an impulse for various authors to develop some very general fixed point theorems for single- and even multi-valued functions of ultrametric spaces.

In this expository talk, which is appropriate to a general audience, we will give an overview of the most important results in this area, entering also into their applications in valuation theory and the construction of Hahn structures.

Date received: April 30, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-41.