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
KeywordsBanach contraction, Banach contraction mapping theorem

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