## Document Type

Report

## Source Publication Title

Technical Report 154

## Abstract

Suppose (X,d) is a metric space, h > 0 and T: X -> X. We shall use the notation T E E(h) to mean [see pdf for notation] for each x,y E X. If h > 1, then T will be called an expanding map. Clearly T E E(h) implies T is a 1-1 function and [see pdf for notation] for each x,y E T(X). In this paper some conditions are found to insure that an expanding map will have a fixed point. It is shown that each finite dimensional Banach space X has the following property: each continuous and expanding map from X into X has a fixed point. It is also shown that not all infinite dimensional Banach spaces have the above property.

## Disciplines

Mathematics | Physical Sciences and Mathematics

## Publication Date

3-1-1981

## Language

English

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Williams, B. B. and Gillespie, A. A., "Fixed Point Theorems for Expanding Maps" (1981). *Mathematics Technical Papers*. 143.

https://mavmatrix.uta.edu/math_technicalpapers/143