A "Converse" of the Bananch Contraction Mapping Theorem

TitleA "Converse" of the Bananch Contraction Mapping Theorem
Publication TypeJournal Article
Year of Publication2001
AuthorsPascal Hitzler, Anthony K. Seda
JournalJournal of Electrical Engineering
Pagination3-6
KeywordsBanach contraction, Banach contraction mapping theorem
Abstract

We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T1 topological space and f: X -> X is a function with the unique fixed point a such that fn(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).

Full Text

Pascal Hitzler, Anthony K. Seda. 'A 'Converse' of the Banach Contraction Mapping Theorem.' Journal of Electrical Engineering Volume: 52.10 2001: 3-6
research center: Knowledge Engineering Lab