A proof of the Generalized Banach Contraction Conjecture-Reference-Cited by-同舟云学术

A proof of the Generalized Banach Contraction Conjecture

Published:2003-02-26 Issue:12 Volume:131 Page:3647-3656
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Arvanitakis Alexander

Abstract

We introduce the notion of J J -continuity, which generalizes both continuity and the hypothesis in the Generalized Banach Contraction Conjecture, and prove that any J 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2003-131-12/S0002-9939-03-06937-5/S0002-9939-03-06937-5.pdf

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