A proof of the Generalized Banach Contraction Conjecture

Arvanitakis, Alexander

doi:10.1090/S0002-9939-03-06937-5

A proof of the Generalized Banach Contraction Conjecture
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by Alexander D. Arvanitakis

Proc. Amer. Math. Soc. 131 (2003), 3647-3656

DOI: https://doi.org/10.1090/S0002-9939-03-06937-5

Published electronically: February 26, 2003

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Abstract:

We introduce the notion of $J$-continuity, which generalizes both continuity and the hypothesis in the Generalized Banach Contraction Conjecture, and prove that any $J$-continuous self-map on a scattered compact space, has an invariant finite set. We use the results and the techniques to prove the Generalized Banach Contraction Conjecture.

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