Title | A "Converse" of the Bananch Contraction Mapping Theorem |

Publication Type | Journal Article |

Year of Publication | 2001 |

Authors | Pascal Hitzler, Anthony K. Seda |

Journal | Journal of Electrical Engineering |

Pagination | 3-6 |

Keywords | Banach 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 |

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