A proof of the Generalized Banach Contraction Conjecture
Authors:
Alexander D. Arvanitakis
Affiliation:
MPLA, Department of Mathematics, University of Athens, 15784 Panepistimiopolis, Athens, Greece
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.