|
|||||
|
|
A proof of the Generalized Banach Contraction Conjecture |
|
| Authors: | Alexander D Arvanitakis |
| Institution: | 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. |
| Keywords: | Fixed point GBCC Banach Contraction Principle scattered compact |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 | |