@article {895,
title = {A "Converse" of the Bananch Contraction Mapping Theorem},
journal = {Journal of Electrical Engineering},
year = {2001},
pages = {3-6},
abstract = {We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T_{1} topological space and *f*: X -> X is a function with the unique fixed point *a* such that *f*^{n}(*x*) converges to *a* for each *x* is a member of *X*, then there exists a distance function *d* on *X* such that *f* is a contraction on the complete ultrametric space (X,d) with contractivity factor 1/2. We explore properties of the resulting space (X,d).},
keywords = {Banach contraction, Banach contraction mapping theorem},
author = {Pascal Hitzler and Anthony K. Seda}
}