TY - JOUR
T1 - A "Converse" of the Bananch Contraction Mapping Theorem
JF - Journal of Electrical Engineering
Y1 - 2001
A1 - Pascal Hitzler
A1 - Anthony K. Seda
KW - Banach contraction
KW - Banach contraction mapping theorem
AB - 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).
ER -