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A proof of the Generalized Banach Contraction Conjecture
Author(s):
Alexander
D.
Arvanitakis
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3647-3656.
MSC (2000):
Primary 05C55, 47H10
Posted:
February 26, 2003
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Abstract:
We introduce the notion of  -continuity, which generalizes both continuity and the hypothesis in the Generalized Banach Contraction Conjecture, and prove that any  -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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Additional Information:
Alexander
D.
Arvanitakis
Affiliation:
MPLA, Department of Mathematics, University of Athens, 15784 Panepistimiopolis, Athens, Greece
Email:
aarvan@cc.uoa.gr
DOI:
10.1090/S0002-9939-03-06937-5
PII:
S 0002-9939(03)06937-5
Keywords:
Fixed point,
GBCC,
Banach Contraction Principle,
scattered compact
Received by editor(s):
May 22, 2002
Received by editor(s) in revised form:
July 9, 2002
Posted:
February 26, 2003
Communicated by:
John R. Stembridge
Copyright of article:
Copyright
2003,
American Mathematical Society
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